The gated town of Sapir (~2.5 days' walk southeast from Mitzpe Ramon) can hardly be called a town it's so small, but it's a friendly community worth visiting (and has the only supermarket in that area that I'm aware of). Outside of town on the northeastern side, there's a McDonalds too, if you need to refill your bloodstream with saturated fat.
In town, there's a family-owned Bed and Breakfast called "Shanti Eleganti" with several suites and a bedouin-style room that will sleep 10. There's no information on the site in English, but the contact info is legible. On the northeastern edge of town there's also a grassy oasis with a pond where camping is allowed.
In the farming community (moshav) of Faran (~1-2 days south of Sapir), there's a hostel called Han Aviran (eng) (heb) There are two grocery stores in Faran; one catering primarily to the Thai population of the community.