No city in Peru caters more to tourists. Avoid Gringo Alley & the central plaza unless you enjoy touts & scam artists. Once you walk a few blocks away from the centre, you can relax.
Cuzco is a great place to hang out. There is a lot to do, a lot to see.
At 3326m, you may need a couple of days to acclimatize to altitude, especially if you fly from Lima. On the other hand, if you travel to Arequipa from Cuzco acclimatization for a climb to near 6000m will be much easier.
Map of Cuzco.
Accommodation in Arequipa 2230m (pop. 700,000)
What a great tourist town! We like it even better than Cuzco. Mellower. Less tourist infested.
Wonderful terrain, one of the best museums in South America, the monastery of Santa Catalina, colonial architecture, the huge Misti volcano looming overhead. Wow!
Check an up-to-date general guidebook when choosing accommodation in Arequipa. There are good hotel options at every price range. Seems everyone we talk to is happy with whatever accommodation they booked. No one hostel dominates here yet with cheap dorm beds.
Before you check in, ensure they will store your extra luggage & valuables safely until you get back from the hike.