A few additional comments on Cuzco and Machu Picchu (as I don't know much about the redemption rules for either AA or UA): Fly LAN if possible. I say this because we got stuck in Cuzco for an extra night when all TACA/Avianca flights (in fact, all flights except LAN) were canceled due to poor weather. The TACA staff helpfully explained that LAN has better technology on their planes (I'm assuming ILS?) that allows them to fly when other airlines are grounded. We wanted to fly LAN in the first place, but ended up on TACA for a host of reasons (long story). Anyway, fly LAN, i.e. use AA miles.

As for staying in Cuzco, the best hotel in town is Palacio Nazarenas. Consider it the luxury wing of the Monasterio (which is next door); also not bad but suffers from tour groups. Haven't stayed at the Marriott so I can't comment.

We took the Hiram Bingham train to MP, which was a fantastic experience. There are plenty of other trains as well, but we thought the HB was worth the expense. There's an Orient-Express hotel right at the MP entrance (not in Aguas Calientes), but we didn't stay there so I can't comment.

Overall MP, the Sacred Valley and Cuzco are an amazing experience and well worth going to!