Cuzco, Peru (population 350,000) is one of the most important tourist destinations in South America:
capital of the Inca Empire
archaeological capital of the Americas
jumping off point for Machu Picchu & the Sacred Valley
Festival Inti Rymi & Festival del Carmen
colonial buildings & pedestrian walks
Inca stonework
Check a general guidebook for the most recent accommodation recommendation in Cuzco. We would e-mail a few days ahead to reserve a bed in one of the more popular hostels, especially during high season.
Budget hostels in Cuzco start at less than US$5 / person for a dorm bed.
We stayed at the most popular backpacker spot, Hostal Resbalosa. (No e-mail address for this one, it seems.)

Cuzco view from Hostal Resbalosa
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 few days to acclimatize to altitude.
Map of Cuzco.
Accommodation in Arequipa 2230m
What a great tourist town! We like it even better than Cuzco.
Wonderful terrain, one of the best museums in South America, the monastery of Santa Catalina, 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.
Before you check in, ensure they will store your extra luggage & valuables safely until you get back from the hike.

Arequipa
Accommodation in Cabanaconde 3290m
Right on the canyon, the trailhead village is a friendly spot. f you want to stay over, perhaps to acclimatize, try the very economical Villa Pastor Hostal (US$2 / single room without bathroom) on the plaza. (You must forgive them the flashing restaurant sign on the roof, ruining the lovely ambiance of the plaza).
There are other options, some off the plaza which is very noisy. No bus can depart town without honking the horn for 10 minutes.
Like many others, we were disappointed with Hostal Valle del Fuego. It looks cool, but ... no. Give it a miss.

Condor statue in Cabanaconde plaza
Accommodation in Andagua
Most hikers are happy to get on the afternoon bus back to the big city, Arequipa. But you can stay over in Andagua if you wish. It has a couple of basic hotels with cold water.
Accommodation in Chivay 3700m
We did not stay there. Cabanaconde is much more convenient for hikers.
But Chivay does have good hot springs. And you can rent mountain bikes there for US$10 / day to cycle the canyon rim.
We had drinks with a reformed Austrian-Australian travel guide book writer who likes to hike down into the canyon from Chivay definitely off the usual gringo trails.