Lake Titicaca is the highest navigable body of water at 3800m. For the natives in pre-Columbian times this was where the gods created the world. Several islands and pre-Columbian sites can be found in and around the lake. The islands have kept some of the original lifestyle and most of the islands are terraced.
I visited on a day trip from Puno. This is part of the standard tourist itinerary in Peru and the boat's passengers came from all over the world. The boat ride was relatively long and the views I got weren't that great. I like trees and there aren't many covering the shores.
OUV
At least for the Peruvian side it's a bit hard to pinpoint. The floating islands (Islas de las Uros) seem more like a intangible heritage as they need to be rebuild every 30 years. Isla Taquile is too touristy and too modern with very few original sites remaining. It would probably be nice to stay over night and have some time to explore more islands and to venture a bit off the tourist paths. Personally, I preferred the Bolivian side and would recommend a visit here.
Getting There
Puno is the main spot on the Peruvian shores of Lake Titicaca. It is well connected by bus to Arequipa, Cusco and La Paz. When travelling between La Paz and Puno you can combine this with a visit to Copacabana and Sun Island. Alternatively, some tourist agencies offer a stop in Tiwanaku. I opted for Bolivian Hop as they do not include a tour guide (appreciated) and focus on the transfer. When transferring to Cusco consider using a tourist bus so you get see some of the sites in between.
From Puno daily boat tours leave to Uros, Taquile and Amantani. To visit Amantani you have to stay overnight. There are also regular ferries, but it's hard to figure out their schedule. Booking and paying an organized tour in the hostal was way easier. For Uros note that it's nowadays more of tourist entertainment complex than a self sufficient island nation. You will get a presentation from the island settlers and be offered goods to buy. I wasn't really into that. In a way it's a bit tragic, that tourism is needed to enable this lifestyle, but that it's also destroying the traditional ways. The most obvious sign is the overweight of most settlers on the islands.
While You Are There
Puno also boasts three Qhapaq Nan locations. I didn't have to time to go there. Presumably it would be safer to go by cab as these locations are in the suburbs.
Notes
The toilet situation is fairly difficult. Bring hand sanitizer and tissues.
Do not stay in Juliaca for whatever reason. It's a terrible place and considered dangerous as soon as you leave the cab and the cab is not parked directly at the airport entrance. The underlying cause are massive smuggling operations in drugs, gasoline and further products centered in the city.