While the name literally means "Center", this district loses out in prestige (if only very slightly) to neighboring Chiyoda, home to the Emperor among others. Still, the Ginza is generally reckoned to have the most expensive real estate on earth and there are plenty of bright lights... and a famous fish market too.
Get in 
The western edge of Chuo starts on the Yaesu (east) side of Tokyo Station, and if your legs are feeling up to it, you can get pretty much anywhere worth seeing within a 45-minute walk. Otherwise, take the subway.
- Tsukiji Fish Market (築地市場 Tsukiji-shijō), 5-2-1 Tsukiji (Tsukijishijo Station, Toei Oedo Subway), ☎ +81 03-3542-1111. Outer Market 5 AM-1 PM, Wholesale Market 9 AM-1 PM, Tuna Auction 5 AM-6:15 AM; closed Sundays, holidays, and the second and fourth Wednesdays of each month. More properly the Tokyo Metropolitan Central Wholesale Market, the famous market is worth a visit for 1600 stalls of bizarre sea creatures, including large blue fin tuna, live shell fish, deep sea crabs, eels and salmon. As you might expect everything is covered in slippery sea water, so choose footwear accordingly. To avoid obstructing traffic, you should not bring large bags or suitcases. Also, watch out for water (often with blood) splashing from containers being moved. It is very busy but the locals don't mind visitors and photographs (no flash), as long as you stay out of the way and don't get in the way of business. Get here as early as possible, which means a taxi if you want to see the auctions, but much cheaper and quite acceptable alternative is to take the first subway in the morning around 6.
Hibiya line Tsukiji station is a short walk away, while O-Edo line Tsukiji-shijo drops you right next to the action. While the market stays open until 1PM, the action drops off after 8AM and many shops close after 10AM or so. Note that the wholesale market inside Tsukiji is off-limits to visitors until after 9 AM, although visitors are welcome to visit the outside market when it opens from 5 AM. Free.
To visit the morning tuna auctions, it is important to get to Tsukiji as early as possible, as there is a daily maximum of 120 visitors allowed into the tuna auction whenever it is held. Viewing tickets are issued on a first come, first serve basis beginning at 4:30 AM at the market's Fish Information Center, located next to the Kachidoki entrance. The first 60 ticket holders are able to view the auction from 5:25 AM until 5:50 AM, while the other 60 ticket holders can view the remainder of the auction from 5:50 AM until 6:15 AM. Visitors must adhere to strict rules when viewing the auction, including no flash photography, no touching the fish, and no actions that would otherwise interfere with any auction-related activities. Note that the tuna auction may still be off-limits during busy times of the year.
A few tour companies do advertise tours that include visits to the tuna auction, but with the disclaimer that it may not be possible to see it if it gets too crowded.
Current plans call for Tsukiji Market to close in 2015. Market operations would move to a larger facility in Toyosu that is currently under development.
- Tsukiji Hongwanji, 3-15-1 Tsukiji (accessible from Tsukiji (Hibiya Line) or Tsukiji-shijo (Oedo Line)), ☎ +81 03-3541-1131. A Jodo Shinshu temple just a few blocks away from the fish market, worth seeing because of its unique, South Asian-inspired architecture. Buddhist services are held in English on Saturday evenings.
- Tokyo Stock Exchange, 2-1 Nihombashi Kabutocho (accessible from Kayabacho (Tozai and Hibiya Lines) or Nihombashi (Asakusa Line)), ☎ +81 03-3665-1881. Tokyo's stock exchange, while one of the largest in the world by capitalization, is now entirely automated, and the tiny building it resides in is mostly for show, featuring a small museum, exhibition hall, and broadcasting facilities.
- Hama-rikyu Gardens (浜離宮恩賜庭園), 1-1 Hama-rikyu Teien (7 min walk from Shinodome, Tsukiji-shijo or Yurikamome subway stations, 10 min. walk from JR Shimbashi station), ☎ +81 03-3541-0200. Originally built by 17th-century shoguns for their private enjoyment, Hama-rikyu is now a public walking garden with an all-season range of flowers and flowering trees. The highlight is the tea house, picturesquely set on a small island in the middle of a pond, where green tea and sweets are available for ¥500. The garden is located next to Tsukiji fish market. A boat which runs up the Sumida River to Asakusa departs from inside the park. Park admission ¥300 (age 65+ ¥150, primary school children free).
- Tokyo Kūa, right under the Yaesu entrance to Tokyo Station. Daily 6AM-11PM. The self-proclaimed first sauna and spa in Japan, still going strong. Open for men only. Entry ¥2300.
- Tsukiji Outer Market. The Outer Market of the Tsukiji Fish Market, the same set of alleys housing Sushidai and Daiwa Sushi, contain a bewildering array of shops. One shop carries nothing but dried seaweed, another knives, another is just bowls of all shapes and sizes! After you've had your sushi breakfast, wander around these shops and pick up something interesting.
The Ginza, covered in its own article, is one of the world's most famous (and most expensive) shopping districts.
Past Tsukiji on Harumi-dori is the island neighborhood of Tsukishima (月島, "Moon Island"), known mainly for its many restaurants serving monja-yaki (もんじゃ妬き). It's like okonomiyaki, but the dough is much more runny and the ingredients are finely chopped, leading to what looks like a puddle of vomit. Just remember the essentials: you form the shredded cabbage into a ring on the griddle and pour the leftover liquid in the middle, and you use the tiny spatulas to press the mixed batter onto the griddle until it sizzles, then eat it right off the spatula. (Most shop staff will be more than happy to assist.) Sounds strange, doesn't it? It is. To get here, take the Yurakucho/O-Edo Line to Tsukishima station, and you'll find "Monja Town"  aka Nishinaka-dori (西仲道り) extending out from near exit 7, with no less than 70 restaurants crammed into a couple of city blocks.
- Oshio Honten (おしお本店), Tsukishima 3-17-10, ☎ 03-3531-7423. The original shop of one of the better-known chains here, with half a dozen restaurants. Try the mentaiko-shiso monja with cod roe and perilla, which tastes oh so much better than it looks. Monjas from ¥1000 up (serves two).
The northern section of Tsukishima is named Tsukudajima (佃島), and is the origin of tsukudani (佃煮), a way of preserving food by simmering it in a sticky soy and sugar sauce. This has fallen out of style in most of Japan but is still commonly available here. Seafood, seaweed (konbu) and various vegetables are the most common ingredients, but if you're looking for something more interesting, try inago (いなご) tsukudani, made from locusts!
- Yoshinoya Tsukiji Store No. 1 (吉野家築地一号店 Yoshinoya Tsukiji Ichigō-ten), Tsukiji 5-2-1 (Central Wholesale Market, Food C). Beef bowl fans come here in droves to make a pilgrimage to Yoshinoya's original store, which dates back to 1926. (Yoshinoya actually opened in Nihombashi around 1899, but along with the entire fish market, they moved to Tsukiji after the Great Kanto Earthquake.) The interior is done up in old Edo style, looking more like an upmarket sushi shop than fast food, and the menu is limited to one main dish only: beef bowl (牛丼 gyūdon) for ¥380 yen, plus optional sides like egg, miso, pickles etc. Opening hours are the same as the Tsukiji Market, and you'll probably need to ask for directions to find it in the vast bowels of the market.
Try a sushi breakfast at Tsukiji. The fish is guaranteed to be as fresh as possible and the prices, while not cheap, are surprisingly affordable given the extraordinary quality - figure on ¥2000-¥3000 for an omakase set of whatever is good today. For comparison, a meal of a similar caliber in the Ginza would easily cost over ¥10,000.
Tsukiji's restaurants can be found in alleys of Building 6, reached by walking in from the main entrance and turning right at the central square. The following two sushi joints are very popular, so be prepared to queue on weekends (an hour's wait is typical) unless you get there very early. Smaller groups may be served before larger ones. Both make a point of serving only fresh fish that has never been frozen.
- Daiwa Sushi (大和寿司) , ☎ 03-3547-6807. 5:30AM-1:30PM. The larger of the two, so the queue moves faster. The standard omakase course is ¥3500 (7 pieces & 1 roll), and a cheaper ¥2100 version also available. Famous for their meltingly soft anago (conger eel).
- Sushidai (寿司大) , ☎ 03-3547-6797. 5AM-2PM. ¥3900 for day's set (10 pieces & 1 roll), of which you get to choose the last piece. They also have a cheaper ¥2500 version.
Quite a few other sushi places can be found in the streets outside the market.
- Sushizanmai (すしざんまい), 11-9 Tsukiji (near Shin-Ohashi-dori/Harumi-dori crossing). The self-proclaimed "King Of Tuna", this is now a large chain but they originate from here in Tsukiji, where they have no less than 7 locations and the three-story Honten is open 24 hours. Prices are per roll and range from ¥100-500, or order a set meal for ¥3000. They have an excellent English menu.
The Ginza has a large array of drinking establishments, most of which are also extremely expensive. This is where the Japanese horror stories of $100 for a beer originate from. Choose carefully, or head elsewhere.
- Sumisho Hotel, 9-14 Nihonbashi Kobunacho, ☎ +81 03-3661-4603, fax: 03-3661-4639. A ryokan style hotel in walking distance from Tokyo Station, Japanese style rooms and big traditional bath available. Singles start at ¥7000, doubles at ¥11,000.
- Hotel Kazusaya (かずさや), 4-7-15 Nihombashi-Honcho (near Shin-Nihombashi Station, Sobu Line), ☎ +81 03-3241-1045, e-mail: email@example.com. Singles ¥8000-9000, doubles ¥14,700.
- Tokyu Stay Nihombashi, 4-7-9 Nihombashi-Honcho, ☎ +81 03-3231-0109, fax: +81 03-3231-0112. Slight discounts are offered for extended stays. Part of the Tokyu Stay chain, these hotels are popular with business travelers. The small kitchenettes, washer/dryers, and free LAN access in all rooms makes these a good value. Singles start at ¥9,450, twin rooms ¥17,850.
- Tokyu Stay Higashi Ginza, Tsukiji 4-11-5, ☎ +81 03-5551-0109. Part of the Tokyu Stay chain. Free internet access, microwave, washer-dryer, and kitchenette in each room. Good staff, views of nearby temple. Located very close to Tsukiji fish market, avoiding an early morning taxi ride. Singles from ¥9400, twins from ¥14,700 per night, breakfast included. Discounts for extended stays..
- Royal Park Hotel, 2-1-1 Nihonbashi-Kakigara-cho, ☎ +81 03-3667-1111. Five-star luxury hotel, adjacent to Tokyo City Air Terminal (TCAT) via skybridge. Suitengumae Subway Station is underneath the hotel.