I've never done a game in Cleveland, but have stayed at the downtown Marriott (Key Center) several times. You can walk to the stadium, RnR HOF and the Warehouse District (the bars and clubs).
Chef Michael Simon's joint Lola is within walking http://lolabistro.com/ (and it's on a neat little street with a few other spots worth checking out), Blue Point Grill is good, Osteria di valerio e al is small but nice Italian, Johnny's is more high end Italian and there are several steak houses nearby too.
I always liked the thought of being able to stay right downtown and walk to the game! Let us know how it goes...