In reply to G1000:
+1 for getting reasonably fit before you go. Proper hillwalking (ie 4-5hr+ days with several hundred metres of ascent) would be more use than trying to do lots of running, though if running is all that time allows then it won't hurt. Fitness won't actually help ward off altitude sickness - I've known marathon runners get cracking headaches on first going up high - but having built up your leg muscles a bit and got used to walking all day will definitely help.
Don't underestimate the benefits of acclimatising gradually. If you're doing any exercise at all then the maxim of not sleeping more than 600m higher than the previous night is a good one once you're above 3000m. A good way to fit some of this in would be touring the Bolivian altiplano or the Cusco area. Just don't go back down for more than a day or two before heading up again.
Also good, and well worth doing in their own right, would be some of the many stunning hikes to be had in Peru (not just the Inca trail!! Though it is spectacular if you don't mind traffic). Another vote for Valle de Lares (though it may have changed in the 13 years since I was there, eek!). Basically the Incas built good paths all over the mountains in that are, so any good local agency that does hiking should be able to put something together. In my experience, and this was a few years ago now, local tour/adventure agencies will know much better the less-crowded more interesting options rather than international companies that prefer to offer certain well-recognised destinations. Might be better to ask other travellers for recommendations of good companies in Cusco/Huaraz/Arequipa once you're out there, if you can afford the time.
Anyway, enjoy! I got my first proper taste of mountaineering in Peru, getting to a 5900m summit before I'd even done anything over 3500m in Europe. We would have got to 6000m if it hadn't been for 40cm of fresh snow to break tracks in too... I wouldn't want to repeat the soft boots/old crampons combination though, or the old fencepole I was given as an iceaxe! I'm sure equipment has got more available in the intervening years...