Arequipa is at 7500' of elevation, whereas Cusco is 11,000 and Rainbow Mtn is 14000. So going to Arequipa for a couple of days really helps you start to adjust to elevation instead of going straight to Cusco. Plus, Arequipa is the food capital of Peru and has lots of "picanterias" which are traditional Peruvian restaurants. I could give you some recommendations if you want them and end up going. It also has the prettiest Plaza I've seen anywhere, and some of the best shopping for artisan souvenirs. It also has some cool things to see, like the original Incan mummy that taught us alot about their religion, and a monastery. Arequipa is a nice, relaxing city before you get serious with your hiking. Pretty LDS temple there too.

Lima, meanwhile, is kind of exhausting because the traffic is so bad.