The ride to Fujigaoka takes about 65 minutes from the airport and costs 1400yen per person. Using the Higashiyama (yellow) subway line, Fujigaoka is 26 minutes from Nagoya Station and 21 minutes to Sakae, Nagoya's main shopping area. It is the last stop on this line.
Fujigaoka is known for its cherry blossoms (sakura) trees in the spring. The streets are all lined with them and it is really beautiful. It is also known as a link city to the site of the 2005 World Expo held in Nagakute town, just a 15 minute linear motor car (Linimo) train ride from Fujigaoka station. The Expo site is currently being converted into a large park area, though construction is not yet complete.
This quaint little area at the edge of town has a plethora of shops, boutiques, patisseries and coffee shops. They also hold a market the 3rd Sunday of every month. From here, take any number of buses to nearby Nagakute town where you can tour the Toyota Car museum, see a historical recreation of a Meiji era battle or go to a "supersento" multi-story public bath complex.
There is a great yakitori restaurant under the subway rail (about 3 blocks south of Fujigaoka station) called Yakyu-dorii. It is almost always crowded and serves really good grilled meats, veggies, and great atmosphere.
Because of the many universities nearby, Fujigaoka has always had a variety of drinking and late night eating establishments. Though they change regularly some of the mainstays are (as mentioned above) Yakyuudori, Ninjoyatai, Jack's Inn, Sannomaru, Tsuki and the takoyaki place on the corner across from MUFG. Recent favorites include Zizi and the new Mr. Donut.
In the street, on a park bench or in one of the two or three business hotels near the station. Otherwise, catch the last train into Sakae where there are hundreds of hotels ranging from the 5 star Tokyu Hotel to the 2 star business capsule and all night sauna Welbe.