in cuzco you can hangout an get drunk/ coked up all day if you want, but yeah it would be a waste not to go to machu picchu or the sacred valley, and teh altitude could be a problem if you're not in decent shape (altitude sickness gives you the worst hangovers-- you need a couple of days to acclimate). but the area around the plaza is pretty lively.
lima is great for food lovers, though as a city itself it's not much to write home about (sprawling, chaotic, ugly). but if you focus on the food it's fucking paradise. will cost you money though because the best restaurants are not cheap.
i'd stick to uruguay then. yes it's going to be more "european" and probably more of a pleasant city to hang out. so is lima for that matter-- i mean in lima there will be more brown people but latin america was european colonies and that's what you'll find-- western culture.
the cuzco region on the other hand remains the heart of quechua culture, so there will be plenty of other stuff to see if you feel like an anthropologist. cuzco has
a decent little football team too. actually,
more than one (this last one is new and at the top of the table, but the other one is over 100 years old)
but for what you want, i think montevideo is the way to go, different without being too unfamiliar, plus it's manageable in just a week. mexico city, on the other hand, is not a city, but a planet.