Salt's eating scene is modest but genuine. The town has a handful of local restaurants serving Jordanian home cooking — mansaf, maqluba, grilled meats — rather than tourist-oriented menus. The area around the old souq has the highest concentration of places to eat, and prices are well below what you would pay in Amman.
Coffee houses are a better bet than restaurants for getting a feel for local life. Older men gather in them through the morning and afternoon, and strangers are generally welcomed. Expect to be offered tea or coffee without prompting.