Call Bodhi about BYO policy. For some reason, I think BYO is not allowed in Houbytown (Berwyn.) I might be totally wrong, but for some reason, I think it's against the ol law.
I'd do Bodhi
Some other joints worth a look
Klas - do a search
Al's for red sauce (Get the eggplant parm)
Depot Diner
Czech Plaza on Cermak
Cheap Mexican at Zacatacos on Cermak. They have a limited beer selection, and char grilled steak tacos. Many of the menu items are pretty decent for the price. Enchiladas in salsa roja can be a great delicious value when they are on their game. Char grilled steak tacos, nicely earthy salsa de chile arbol, and usually sizzlin hot salsa verde. I like this place a lot.
Riverside Family Restaurant - 34th and Harlem. Diner with a Bohemian / Eastern Euro tinge to it. I'd definitely get a fish dish. Oddly enough, I think they are really serious about fresh fish specials. Others rave about the place too. The menu has landmines, but if you know what to order, you will eat like a king for the price.
Further out, but lth love has been given to:
BYO Yum Thai on Madison in Forest Park
Jimmy's place on Madison in Forest Park as well
PLenty of love has been given to Villa Nova's pizza too. You won't be far at all. They might allow outside beverages.
We cannot be friends if you do not know the difference between Mayo and Miracle Whip.