Directly across the street from the Frissell Museum [1], stop for a refreshment at the homey Hotel and Restaurant Mitla (Benito Juárez 6, tel. 951/568-0112, 8 a.m.–7 p.m. daily), domain of the sparkplug mother-daughter team of Teresa and Gloria González de Quero. Here you can enjoy Mexico as old-timers remember it, in a charmingly ramshackle hacienda-style farmhouse, where roosters crow, dogs snooze, and guests can have their seasonal fill of bananas, avocados, mandarins, and papayas from a shady backyard huerta (orchard). Their 16 rooms ($15 s, $22 d) vary. Most rooms in the upstairs tier—plain but clean, with the essentials, including hot water—are acceptably rustic. Parking is included.
Across the plaza from the museum is the new four-star neo-colonial-style Don Cenobio Banquet Salon and Hotel (3 Calle Juarez, tel. 951/568-0330, fax 951/568-0050, informas [at] hoteldoncenobio [dot] com, www.hoteldoncenobio.com [2], $70 d), with about 20 beautifully decorated rooms built around a large, inviting grassy green pool patio. It has a wealth of facilities, including a restaurant and banquet hall for 500 people. Rooms come with air conditioning, cable TV, queen and king-sized beds, and much more. The only drawback to all of this is that they rent the place out to hundreds for conferences and parties quite often. Best to check by telephone before reserving an overnight.
Alternatively, about five blocks north, closer to the archaeological zone, try the family-run 
Hotel and Restaurant La Zapoteca (5 de Febrero 12, tel. 951/568-0026), on the right just before the Río Mitla bridge. The spic-and-span restaurant (7:30 a.m.–7 p.m. daily), praised by locals for “the best chiles rellenos in Oaxaca,” is excellent for meals, and the 20 clean, reasonably priced rooms ($15 s, $20 d, $27 t), with hot water and parking, are fine for an overnight.
Links:
[1] http://www.moon.com/destinations/oaxaca/oaxaca-valley/east-textile-route/mitla-archaeological-zone/frissell-museum
[2] http://www.hoteldoncenobio.com