Welcome to LTH, Idiosyncronaut!
I'm personally not aware of any good ones in the immediate 'hood (though I've no doubt some exist), but you have a couple of board favorites not too far away, depending on where you are, precisely.

There's a Jay's up on North Avenue, a few blocks west of Damen, and while it's not a personal favorite it's a solid beef and well-loved by many folks around here.

Also, Boston's is pretty close, where Chicago and Grand intersect (couple blocks west of California). That's another board favorite.
Hope one of those is close enough for you. Be sure to report back, and welcome again!
Jay's Beef of Chicago
2255 West North Avenue
Chicago, IL 60647
773-772-2333
Bostons Italian Beef
2932 W. Chicago Ave.
Chicago, IL 60622
773-486-9536
Dominic Armato
Dining Critic
The Arizona Republic and
azcentral.com