A full day's trip takes you to Isla del Sol and Isla de la Luna off the coast of Copacabana. The islands of the sun and moon are some two hours journey beyond the outcrop of the Bolivian coastline and the boats take a zigzag route from Copa to north Sol, to Luna, to south Sol and back to Copa, all of which costs about 20 bolivianos per person.
From Copa's tiny "harbour", collect a boat (you can either pre-book with the tourist offices on the main street by the market or chat to the captains to find out at what time they leave and then turn up - the price is pretty much fixed). No self-respecting boat ever leaves on time but eventually you'll head off on the crystal clear waters, past the tiny naval HQ (land-locked Bolivia has one solitary sea-going vessel, the Libertador Bolivar, which is kept docked in Argentina and patrols the Plate River between Argentina and Uruguay, but the HQ flies a flag and is spick and span) and eventually land on the northern end of Isla del Sol. The boats all pass through the small collection of uninhabited islands formed between the very end of the Bolivian mainland and Sol. The journey is relatively uneventful and there's little entertainment unless you're prepared to go out on deck to catch the (scorching) rays - remember the thinness of the atmosphere at 4000m will mean you tan (and burn) even more quickly.
On Sol, it's a fairly gentle walk/climb from Challapampa (past some great sights like cows and bulls grazing or being watered on the lake-side) up to the labyrinth ruins at Chincana (the 20 Bolivianos entrance ticket covers both this and the mini-museum dedicated to the Atlantis discovery north of Sol where submerged buildings became more interesting when gold coins were discovered in the 1980s - excavations continue). (It’s worth noting that the loos next door to the museum are both fairly clean and free - visit them on your way back though as there are not many and the queues when the boats dock are huge). When you’re done at the deceptively large but ultimately unsatisfying ruins, you can either then walk across the island/stay the night or re-catch the boat to head to Luna (in my view, not a worthwhile use of your time save for the better view of the Cordillera Real behind Luna), and then the boats backtrack down to the south end of Sol and stop in for half an hour at the most at the little town of Yumani. Here, you can climb up through the gardens next to a babbling waterfall, buy the usual array of jumpers and wares and perhaps meet a particular young lady and her tethered accomplice - "Fotografia con una llama senorita? Un dollar".