For a night stop between flights I've used the FM7 "resort" a few times. The room rates have crept up to the £50 mark, but they include an airport pick-up, booked in advance and so (in theory) tailored to you and your arrival time.

IBIS have a couple of "airport" hotels, one very cheap (Ibis Budget), the other (Ibis Styles) more fancy. The shuttles were at two hour interval though. Taxis are inexpensive, though for many there's comfort in using the(higher cost) limo services that have desks in the arrivals area. Most of the taxi firms will have kerbside dispatchers who can be very helpful: Bluebird is the traditional favourite, but popularity means it can get overerwhelmed. Uber/Grab are available and there was a kerbside "help" area where agents were helpful in sorting out reservations.

For more mainstream, big-brand accommodation without going all the way into the city, there's a very good value Hilton Garden Inn (£40/50) attached to a Mall in the new(ish) development Taman Palem about five or six miles from the airport. You'd need a taxi.

If you want a quick taste of the city, the train will get you there quickly, safely and cheaply. The BNI City station has a Holiday Inn Express close by, just off JL Sudirman (the main central Jakakarta avenue) and close to the smart malls.

There was, maybe still is, a hotel somewhere in one of the terminals. I've no idea wha it's like.