I am looking for private rooms, and possibly a step up from backpackers but still cheap.

"Cheap"is a relative term. I stayed at Bamboozi Lodge in Tofu in October and I thought it was fairly cheap: I paid 1500 meticais per night for an A-frame chalet. That's around about £30-ish, depending on the exchange rate. Dunno what your budget's like but the chalet would sleep 4 so I thought that was pretty good value.
We stayed in a guesthouse on the beach in Tofo, 1300 Mtn, breakfast included, it's a new place, give Dona Laura a call 828215921. This is cheap in Tofo, especially if you are not into the ususal backpacking places (Fatima's, Bamboozi etc.)
Very nice is Baia Somnambula but expensive (around 3000 Mtn for a night): 828215587
XaiXai don't know very well, along the beach there are various anonymous (not signposted) places to stay, I guess they will be all around the 1500 - 2000 Mtn price range.