For future hotel reference, I stayed at Gringo Bill's when I was there last winter. Clean, serviceable, and free breakfast. I think rates were in the less than $100USD per night.
They had some sort of bag storage at MP before the entrance due to a bag restriction within the site itself.
Aguas Calientes doesn't have much other than the hot springs as far as I was concerned. Spent 2 days wandering through MP and was glad to have the 2 days rather than just one.
As for Cuzco vs Lima. Lima had excellent seafood if you like seafood. Try the ceviche. Cuzco museums were great too. Personally I love museums more, so I'd spend more days in Cuzco.