There are homestays all over Indonesia. I don't recommend using Booking.com or Hostelworld to find cheap accommodation - you'll find cheaper results on Google Maps, and you'll be supporting local homestays that may not be registered on the big websites.
You can find homestays easily by zooming in on any city or town and searching homestay. If you're somewhere remote and no homestays show up, try "accommodation" or "hotel".
Below is an example of this search in the town of Cilacap.
By comparison, Booking.com only shows 19 properties in Cilacap.
If you're looking for budget accommodation, you really don't need to book in advance. You'll only need to make advanced bookings if there's a resort you want to visit or you're after a really nice stay at a specific place, or if you're travelling to a very popular location during a public holiday/school holiday. There's so many accommodation places though, if you're on a budget you'll find heaps last minute.