Accommodation in the Cirque de Mafate is entirely geared toward walkers, so don't expect any hotels. That said, there are now a few comfortable B&Bs in La Nouvelle, Marla and Aurère. Check the Plateforme de Réservation – Île de la Réunion. A few places have camp sites. Bring cash, as credit cards are not accepted.
During the busiest months (October and November), it's best to book your accommodation well in advance.