Cusco has some wonderful hotel options:
I highly recommend staying at the the Hotel Monasterio, a Belmond Luxury Hotel and Resort (formerly Orient Express), located in town at Calle Palacio 136. I have stayed there on both my trips to Cusco.
The rooms are lovely with some having pumped in oxygen to help with the altitude. Don’t miss the lovely small chapel on the premises with its beautiful paintings. El Tupay is the more formal dining room where opera music is performed four nights a week. Even if you don’t eat there, at least stop in after your dinner to have a drink and listen to the music. The Illariy Restaurant is a great spot for the breakfast buffet with both indoor and outdoor seating.
Belmond also has the Placio Nazarenas, located next door to the Monasterio. It is a beautiful, all-suite hotel located in a former convent, with the Senzo Restaurant, their lovely dining room.
Other good options include the Novotel located at Calle San Agustin 239. There is also the Inkaterra La Casona at Placio Nazarenas 113 and the attractive and upscale Placio del Inka at Piazoleta Santo Domingo #259.