The most convenient place to stay is Fitiuta Lodge, in Fitiuta village a short walk from the airstrip. There are eight rooms with shared bath and cooking facilities are provided.
The Ta'u Motel is near the small-boat harbor in Luma village, on the opposite side of the island from the airstrip. It has nine clean rooms with bath and fridge, and you can cook your own food. The entire motel is often booked by local contractors for extended periods, so call well ahead (it can be difficult to get a call through). They can pick you up at the airport for a price which depends on whether they have to go anyway.
The motels on Ta'u are often full or closed, and it might be better to arrange a homestay in advance through the National Park Visitor Center in Pago Plaza on Tutuila.
No restaurants are to be found on Ta'u, only small village stores. If your baggage isn't overweight, bring some food with you on the plane from Tutuila. There's no bakery on Ta'u, so it's a good idea to bring bread from Pago Pago.