The supply is endless
Cusco is chock full of hotels and hostels for every budget. There are over 2,200 options for lodging in Cusco, not counting nearby areas.
There are both luxury and budget options in the center near the Plaza de Armas, though prices do tend to go down as you move away from the center.
If you want a quieter, pedestrian area, look for a place to stay in San Blas. If you’re into nightlife, look at Calle Plateros, Procuradores and Tecsecocha.
Staying right in the centre is of lesser importance in Cusco, which is relatively compact, easily walkable, and well-served by buses and taxis. So there's no need to really agonize over which neighborhood to choose.