Isla del Sol
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 life in the island is tranquil, there is no noise, no motorized traffic and no rubbish on the streets (which is rare for Bolivia).
The only conventional way to get to Isla del Sol is by boat. Numerous tour companies operate full and half-day excursions from Copacabana. You can make reservations at the agencies, or just go down to the waterfront around 8:00 or 1:00. It's also possible to catch boats from Yampupata at the northern tip of the peninsula.
If you don't like to book a tour with a company, you can find a one-way boat to Challapampa (20 Bs, ~2 hours) at the waterfront. You may spend a night in Challapampa, walk to Yumani the next morning and return from there to Copacabana by another boat.
Recommend leaving your large backpack with a hostel in Copacabana as getting up the inca steps in Yumani is hard work at 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.)
Again, Yumani has the best offerings. Challapampa has some restaurants where you can get soup+trout for about a small 20 Bs. 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. 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 many places.
Isla de la Luna is easiest visited from Yumani, by renting a boat.
Be aware of attacking dogs who wanna bite. In case use your backpack for protection and throw stones.