Cheapest cities in Indonesia

The cost of living in any given place is pretty much inversely proportional to how busy the area is, thus the number of possible opportunities for expat employment.

I can share my experience of a small village some short distance from Wonosobo in Central Java, and extremely cheap place to live where my monthly outgoings were around Rp2 million/month. It's a case of you don't spend much when there's nothing to spend it on. Inflation would make that more difficult now, but it could still be done on about 4 million.

I live in a smaller city at the moment, moved mid last year from a town in South Tangerang. There are a couple of international schools here with expat employees, but that's pretty much the limit of expat work, but prices are pretty reasonable. A nice, quite new, fairly large 4+1 (maid room) house with 3+1 bathrooms works out at Rp19 million/year including security and rubbish collection.
A cinema ticket is cheaper, and most take away local food comes in at less than Rp25,000 per person.

Expats wanting to work might well go for the larger cities, but those that can work remotely or don't care about employment would do well to consider smaller towns.

I can't talk about off Java as I have only visited, never lived there.