I've been to Jacobs Progressive Field a few times, though it's been about 5 years since my last trip there. It's nice. Not spectacular, but nice. I remember being impressed with the variety of food available at the various concessions...everything from hot dogs and burgers to pasta and sushi. (Who the hell eats sushi at a ballgame?!) After one of the games I went to, my friends and I went to a place called the Winking Lizard Tavern, which was pretty good as I recall, and it was just a couple of blocks north of the ballpark. There were several other bars nearby as well, all of which were pretty crowded after the games, so I'm guessing they're good places to go to.
If you have time while in Cleveland, check out the Rock & Roll Hall of Fame, about 9 blocks north of Jacobs Progressive Field, up E 9th Street.