Yep. While I was there, I stayed at the Royal Inca Hotel. It was great! They had a wonderful restaurant, a bar, rooms with tv, and it was right accross the street from one of the squares (a couple blocks away from the main square).

I put this on another site after staying there.

From David Cross
Hotel Cusco Plaza II
Address – Calle Saphy 486, Cusco-Peru
Telephone – 51-84-263000
This is a really good place to stay in Cusco, near to the Plaza de Armas and
with a market area nearby.
The staff are friendly and helpful and, somewhat unusually, most rooms have
plug-in heaters.

I have no idea of the cost as we were on an Exodus tour.

I stayed at the Hotel Monasterio, which occupies a 16th century Spanish monastery. It’s probably pricier than other options, but it is elegant and very “colonial”. We stayed there a couple of days before heading out on a plane (then four hour banana boat) ride to the Peruvian Amazon.