Lake Titicaca is located at an altitude of 3812m. With this height it is the highest navigable lake in the world and therefore worth a visit. Peru and Bolivia share the lake. From Peru, Puno is probably your place to be. Puno itself is relatively unexciting and has no highlights of its own, but you come because of the lake. If you want, you can visit Uros Islands and Taquile Island in one day. Be aware that it can be very cold at night in this height. and basic hostels don’t necessarily have heaters in Peru.
Well known are the floating reed islands of the Uros and therefore somehow belong to a visit. But don’t expect too much here, the whole thing is a big tourist show. You come with a small boat to the island. The Uros will show you the island, you might do a tour with a reed boat, the Uros sell things and you go again and the next boat will go to Uros Island.
With a bigger boat you can go to Taquile Island. This is a normal island and much bigger than the reed islands. The island is quite beautiful and it is worth to stroll a little bit over the island. But make everything nice and quiet and don’t overexert yourself. You are here at over 3800m altitude. If you are not used to the altitude, even the smallest hill will be exhausting. From the island you have a great view over Lake Titicaca and in good weather you can see as far as Bolivia.