Cleveland gets a bad rap, though it's not that bad of a city to visit for a weekend if theres a sporting event going on. Went down last October for the ALCS. Cleveland fans are very friendly.
As for some places to check out, Cleveland has a lot of good restaurants and craft beer places. East 4th Street is the happening area before and after baseball games. A lot of good bars & restaurants to check out. The Butcher & the Brewer is a real good spot for snacks and craft beer. The Greenhouse Tavern is a really good spot for dinner as well.
Check out West Side Market one morning/afternoon. Pretty similar to the St. Lawrence Market. As well, the area around there is nice. A lot of good restaurants, bars & patios. Great Lakes Brewing Company is right nearby. As well, ate brunch at the Flying Fig which was a good spot! The Black Pig was also great and nearby as well. Checkout the cocktail bar on top of the Hilton downtown. They make good cocktails and you get a nice view at night of the surrounding area.
Otherwise, never did any of the tourist stuff since we were only there for a weekend. Rock & Roll Hall of Fame I guess is something to see if you have time. Like other posters said, not much happening downtown. It's pretty much a ghost town at all parts of the day.
Cleveland wasn't that bad. I'd go back again to catch some baseball games or maybe a Cavs/Raptors playoff game in the spring or something. Overall, if there really isn't any sporting event thats going on in the city, I wouldn't go out of my way just to visit Cleveland.