Many will probably think this is way too south, but I have been known to be quite the interesting driver
Depending how far north, and off of Western you are, and how you drive, and if the stoplight gods are working with you, this is one of my favorite beefs in the city:
Tore's Italian Beef
2804 N Western Ave
Chicago, IL 60618
If you actually try to get here, get a number, and try calling 1st. I haven't been in a LONG time, and I heard they were closed for remodeling at some point.
Again, it's a stretch south, but I would make an attempt if other options in the area don't pan out. I would consider it a driving challenge to get there and back in your time constraint, but if the driving gods were with you, I'd say it could be done. (probably not on a Friday after 1pm though.)
I like this place because the beef isn't overly salty like most, and when you combine it with the giardiniera (theirs is HOT!!) the salt content balances nicely for me. Most of the beef joints have both salty beef, and salty giardiniera which overkills it IMO.
Maybe try this place on a Tuesday with less traffic. If nothing else, it won't be
BAD.
P.S.Their pizza slices are completely forgettable - although they do make a decent, cheap side for a beef sammich.
We cannot be friends if you do not know the difference between Mayo and Miracle Whip.