My experience is obviously Northeast Ohio and great breweries are abundant. BBQ is not as good as the south but still fine on its own. All would be worth the ride up to this area.
Breweries:
Great Lakes Brewery: Awesome beer, nice brewpub and great food
Brew Kettle: Great Beer and Great food
Market Garden Brewery: Above Average beer, good food
Nano Brew (Owner by Market Garden): Above average beer, better food than Market Garden
Platform Brewery: Really, really good beer. Food is brought in by local restaurants and rotates as they don't have a kitchen.
FatHeads Brewery: Great beer, amazing food
Buckeye Beer Engine: Good beer, great burgers
Hofbrauhaus: Just an amazing all around experience. Beer is good, food is great
Tremount Tap House: Beer is average, food great
Portside Distillery: Average beer, never had the food
BBQ:
Bubba Q's: Really good all around southern style bbq
Mabel's BBQ: Not even sure this is open yet but it's a Michael Symon place that stole my idea of CLE BBQ so I'm sure it'll be a hit
Famous Dave's: It's a chain obviously but I'd say its above average. I pretty much always get their burnt ends and they have really good sauces.
Hot Sauce Williams: Only in the ghetto but damn if it isn't good stuff
Blazin Bills: Average BBQ for the area. Below average when comparing it to real BBQ.
Old Carolina: Another chain place but its not bad, sauces are weak IMO