I was there in April. 2 days in Lima, flew to Iquitos with 5 days on the Amazon, then to Cusco for 3 days, finally to the Inka Trail for 4 days ending with MP, and finally two days in Urubamba before returning to the US.

A couple of thoughts. I stayed in Miraflores, but should have stayed in historic Lima. You didn't ask about the Amazon, so I'll skip those details. I acclimatized in Cusco before starting the Inka Trail. There are some day trips from Cusco, but 1.5 days were work days for me. I did one of the "free" walking tours of Cusco and it was very informative. Not sure how to guide you re: a day trip to MP as I did the trail ending at MP. It appeared that there were a lot of logistics involved re: anything related to the MP and unfortunately it seems as if one is bound by those logistics. I do know that there is a limit of the number of entries each day, so plan ahead.

Let me know if you have any questions.