Wonderburger is worth a stop once it re-opens. It's a nice old-school burger, and the house-cut curly fries are unheard of, and pretty good (if occasionally greasy). Fat Tommy's is a decent alternative, but moreso for its bacon-wrapped Polish than its burgers, which are sometimes good and sometimes way over-cooked. Their wider menu is a relative breath of fresh air in pizza/beef/burger land down here.
Speaking of beef, Pop's on Kedzie is solid. I love their combos, and the hot peppers are unique--fresh, with celery and serranos, not at all oily.
Mini Hut has a new-ish outpost fried chicken outpost further north on Kedzie at 87th that's pretty good--hit it up a few times, pretty juicy and nice crust.
Definitely hit up all the BBQ places.
Pizza: in addition to Nick & Vito's and Fox's (both good versions of cracker crust), there's also Barraco's, Rosangela's (both in evergreen park--Barraco's is related to N&V's, and Rosangela's has a nice, blackened, airy crust and herb-y sauce) and Palermo's (in Oak Lawn--sweet sauce, various thicknesses) all on 95th. Louisa's is another pizza worth eating, but deep dish rather than thin.
In Bridgeview and environs are Chuck's (his BBQ has improved, but isn't amazing, while his Mexican and Southern dishes are gut-busting and inexpensive), Al Bawadi, and Al Mawal for Middle Eastern (meats are often on the overcooked side, but grilled over live wood and thus excellent), and Grand Duke's (absurdly large Lithuanian menu--go for kugelis!)
For a Freddy and other sandwiches, there's Calabria's in Beverly, which is pretty reliable (though it's no Graziano's).
There are countless Mexican places these days, on Kedzie, Pulaski, and Cicero, from 50th on down to about the seventies or eighties, and then more sparsely. You could do a food crawl exclusively on Mexican pollo asado on about a two mile stretch of Pulaski alone. Pozoleria Dona Esther was a recent da Beef recommendation that I thoroughly enjoyed, just off Kedzie on 59th. Stick with pozole.
That's most of the eating that's sustained me throughout my SW-side existence, with some less notable things that I'll try and come up with later. Lemme know if you need more details.