Visit Isla del Sol, an old Inca island in Lake Titicaca -- very peaceful and nice. You can also sleep there. Copacabana is also famous because of its cheap hotels. You can sleep there for a night. And you can eat some vegetarian food in town.
Quick Tips:
Watch the sunset and climb a mountain for a great view.Best Way To Get Around:
Walking. Take boat to get to the islands, Island of the Moon and Island of the Sun (I prefer Island of the Sun).