If you dont want to walk to MP, you can certainly do it in a short time. The only caveat is that you need to get the ticket and res for the train to MP a day ahead of time. So effectively it forces it into a three day trip. I think I spent 5 days in Cuzco and didnt see everything.

But Lima is a mixed bag. I like it there, but I am in a minority. A distinct minority. I wouldnt plan on spending time there if you can help it. The son of the owner of the guesthouse I stayed at in Cuzco liked going down to Arequipa, for what it's worth. Haven't personally been. Whatever you do, if you go somewhere in the Andes, you will be told to take it easy. It's good advice.