Hey - I see it's been mentioned but it's so important I'll say it again - something you absolutely need to keep in mind is the altitude. DO NOT think you're going to just get off the plane in La Paz, nap for an hour, and then start mountain biking around. Unless you live in the Himalayas, you need to give your body a good couple of days - at least - to acclimate. Failure to do so could lead to serious health problems. I had a friend who had to evacuate Puno a couple of years ago because he started getting altitude sickness, and he wasn't even doing anything strenuous, just research work for a grad school professor.
At some point, I'd suggest taking a trip to Lake Titicaca. From La Paz, you can get a minibus that will take you to Copacabana, or you could go the other way and hit the lake from southern Peru. Either way, it's really a beautiful place to hang out, even for 2-3 days.
In Peru, although I've never been, I've heard wonderful things about Arequipa. That might be another city worth hanging out in for a day or two.