Local hotel - don’t expect fancy rooms. Plain, but adequate rooms, breakfast edible, but plain. Air conditioning works (a must in summer). Staff knows enough English to communicate.
Madaba is a small town. Supposedly near airport, but it is roughly equidistant to downtown Amman and a challenge to get to unless you use taxi. We arrived after midnight on a late flight, things were grubby and empty. In daytime, things were still run down and dusty, but Greek St George church is a small jewel, there is an area with tourist shops and a great restaurant down the street from church, Herat Jdoudna (spelling?). If you want a flavor of non-tourist and non-urban Jordan, give it a try.