Problem is a lot of places in that area will be pretty busy on a Saturday night. Here are some that I think will likely be more civilized and with food that's interesting without being too weird. From your description I'm taking "cheap eats" to mean spending somewhere in the vicinity of $80-100 for three people but not $200. If you really want cheaper than that-- like $40-50 for three-- go have Colombian steak at El Llano, I'd say.
Erwin-- a really nice grownup place, near Halstead/Diversey, with reliable contemporary American food. This would be my first choice.
Prego-- a pleasant modern-Italian place on Ashland, opposite the Jewel, tin ceilings and live music (of the one person with a guitar kind). Cozy, decent if not super-accomplished food (if you want that, Merlo a few blocks away on Lincoln would be a better bet, but it's a little more formal feeling).
Glory-- Bucktown restaurant with imaginative comfort food from New England; seems calmer than a lot of noisy Bucktown places although it's quite popular.