Inca legend says that Viracocha, the bearded god who created the universe, emerged from the waters of Lake Titicaca and created the sun at this location.
The son and daughter of Inti were sent out of one of the caves on the island with a golden staff. Manco Cápac took this staff across the water and found Cusco between the mountains. He decided to start his Inca empire there. This of course is according to legend. In reality, Cápac probably lived in the region of Cusco instead.
There are also numerous tour companies organizing full and half-day excursions, you can make a reservations in one of the numerous agencies in Copacabana. It is recommend to leave your large backpack in a hostel in Copacabana as getting up the Inca steps in Yumani is hard work at a high altitude.
There are no motor vehicles on Isla del Sol. It might be possible to rent a donkey.
Unless you're spending the night on the island, your itinerary will be basically determined by the boat tour you arrived on. Frankly, the half-day tour is barely worthwhile as it consists only of a brief stop at the southern end and most of your time will be spent on the boat.
A full-day tour will take two hours to get from Copacabana to Cha'llapampa, two and a half hours to see the museum and make a round trip hike to the Rock of the Puma, three hours to take the boat to Isla de la Luna and back to the Inca Steps at the town of Yumani, and two hours for the ride back to Copacabana. You can also choose to hike from the Rock of the Puma back to Yumani (three hours) and catch the boat from there. (Decide on this when buying tickets, as the boat fare to Isla de la Luna adds just a bit to the cost.)
- Cha'llapampa, the town on the northern end of the island, is where the boat lets you off. The Gold Museum (Museo de Oro) displays Inca treasures which were discovered underwater off the island in the last decade. The Bs5 admission also lets you see the Rock of the Puma. Other than that, the town has a small beach and some dirt roads.
- The sights on the northern tip are ancient Inca sacred sites. The Rock of the Puma, or Titi Kharka, after which the lake is named, is a large formation that will probably look nothing like a puma until the guide points it out. Your reaction will likely either be "Ah, there it is!" or "That's it?!" A short distance from the rock is the Inca Table, a low platform fashioned of stone. You may just be imagining a red tint on it, but it was supposedly used for human sacrifices. The Footsteps of the Sun nearby are a set of natural (or supernatural?) impressions in rock.
- From Yumani on the southern part of the island, the Inca Steps descend down to the water. At the bottom is the Fountain of Youth. (Oh, those gullible conquistadors!) The channel of water flowing down the hill should convince you that drinking from it is much more likely to shorten your life than extend it.
- The Temple of Pilcocaina is a little further south, and is an optional stop for the boat tour. Bs5 admission.
Again, Yumani has the best offerings. Challapampa could be good for lunch if you are coming with the morning boat and staying overnight on the island. Many places in Copacabana will sell you a lunch box, convinient for daytrippers. The few shops around have limited stocks, -fruits are mostly bananas and apples.
Yumani is growing fast and already has a lot of tourist facilities. There are some basic alojamientos in Challapampa and Challa. Challapampa in the northern part is much easier to get to, the village is on the beach and the to accommodation are cheaper. The cheapest hospedajes start at about $2usd per night. At those prices expect basic conditions, everything is pretty clean and decent though. Camping should be possible in Challapampa.
Isla de la Luna is easiest visited from Yumani, by renting a boat.