Great Lakes is an obvious choice but you can get their stuff at any store around here.
Brew Kettle is up in CLE. They just won a bunch of awards at the Berea Oktoberfest. White Rajah is a great IPA but Lupulin Luchador (sp?) is gaining notoriety.
Fatheads has a great and wide selection with a great restaurant.
Four C's is another brewery around here, their place has a selection of their own beers plus many others from prominent breweries in the Midwest.
Buckeye Brewing is good but the Buckeye Beer Engine place is a little sketchy.
Indigo Imp has been popping up more often around here.
Main Street Grille and Brewing Co. has a phenomenal birch beer ale.
Willoughby Brewing might be too northeastern from CLE but it has some great unique beers like the peanut butter porter.
These three might be a bit of a haul:
Lagerheads is out of Medina but Savage Stout and Kilt Em All are some of my favorites.
Thirsty Dog and
Hopping Frog in Akron make some pretty good stuff. It's a 40 minute trip from CLE to Akron. TD has a tasting room, HF has a pretty gourmet brewpub.
I did a brewpub crawl back a few years ago and hit most of these places in a day.

You might have trouble finding somewhere to go on Sunday but a place like Acme will carry all of the local stuff.
Avoid Ohio Brewing Company, they have problems with quality control.