I'm a huge fan of both Honey 1 and Brown Sack. Haven't tried the other two stevez suggested, but appreciate the suggestions.
For other options, I'd also add Jimmy's Red Hots, which is just over a mile due south at 4000 W. Grand. If you're willing to drive to Albany Park (Semiramis, 3 miles) or North Center (Sticky Rice, 2.9 miles), there are several options that are closer and get a lot of attention on LTH, including Hot Doug's (1.9 miles), Kuma's (1.7 miles), Smoque (1.8 miles), Urban Belly (1.7 miles), etc. I've only visited Treat (1616 N Kedzie, 1.4 miles) once for brunch, but that also might be an interesting non-Mexican option. Hot Spot (2824 W. Armitage, 1.5 miles) is also better than passable. And, the Philly's Best (1.3 miles) at 2436 N. Milwaukee has proven to be a reliable, quick spot for a decent meal. The last three listed here likely won't lead to mind blowing culinary experiences - - but they are all satisfying and I'd happily return to any of them.
There are also many Polish and Cuban restaurants not too far from where you'll be, but I unfortunately don't have any to recommend. Perhaps other do, if you'd be interested.