Cleveland is an interesting city. I spent most of my time in what is called the "Ohio City" part of Cleveland, but managed to get out for a day and explore. The city is pretty spread out, so sadly you really need a car to get to the top places.
There are 5 breweries near Ohio City area with another 5 in development, so I think Cleveland as a whole will be more exciting in a years time.
I stayed at the Aloft Downtown Cleveland. Right around the corner from it was the Portside distillery and Portside Brewery, which are set to open any day now.
In a funny twist....and most people don't seem to know this...but a number of the best beer bars and breweries in Cleveland are owned by the same guy.
Sam McNulty opened The Bier Markt years ago and also owns the Market garden Brewery and Nano Brewery, plus some other eateries.
Nano Brewery was tiny, but a lot of fun. Definitely my favourite spot downtown.
Market Garden is bigger...it's kind of the bigger brother to Nano. They test beers at Nano, if they sell well, they may produce them on a larger scale at Market Garden. It had a bit more of a "party" vibe to it, but is right near the market so worth a stop.
Great Lakes was solid. I thought the food was decent, not special. I'd compare their experience to that you get at Mill Street Brewpub but with slightly better beers.
I quite liked The Brew Kettle in Strongsville. Great food and bbq, and a very solid tap list. Probably my overall most enjoyable stop.
Conversely Tremont Tap House was a bit of a let down. Their tap list was on par with Brew kettle, but they had better bottle selection. The service was "meh", and it didn't help that one of the owners/workers was drunk as a skunk with some other workers at the end of the bar. They were doing a private tasting of sorts and he had no quams verbally harassing the staff that were working and, in his own words "being a douchebag".
If I had happened to be seated at a table or on the patio away from that, I would have enjoyed it more and would recommend it as a top place to go.
For cheaper eats with some decent beers, Happy Dog can do the job.
For bottles, the Save on Tobacco in Mentor was great and had a ton of stuff. I also visited the Lizardville bottle shop and Winking Lizard bar in Bedford Heights. A few different selections, but nothing special for bottles that I was looking for.
Never made it to Fat Head's further south, although everyone raved about it. Indigo Imp was closed the day i wanted to stop by. They are quite different as they use open fermentation for their beers.