There are a number of individual private homes or villas available for short or long term stays, ranging from 1 or 2 bedroom up to quite sizeable options for larger groups or big families.
Facilities and quality vary.
There are usually a wide variety of local cafes and restaurants where you can eat out. Otherwise there are local stores (larger supermarkets in Avarua, the capital) where you may buy provisions in order to cook and eat in your own 'home away from home'.