From La Paz, Max and we booked a ticket on Bolivia Hop, a bus for which you can book tickets covering various cities (and you can stay a night or two at each stop if you want). Not a bad system, but not as cheap as local buses would be. But hey! Something to try.
Our first stop was Copacabana at the shores of Lake Titicaca. We stayed for one night, did some kayaking and hiking and visited the Isla del Sol and the Isla de la Luna (a tour with a very high boat to land time ratio. I got a bit sea sick. My head is very sensitive…).