HRCJR gives good recs. Mabel's and Lola are on East 4th street, very close to ballpark. Add the Butcher & the Brewer to that list. Down by the Flats along the river (still walkable but farther from park and stadium), I would go to Collision Bend Brewery (great food too). There is a nice walkway down there along the river and tons of restaurants and watering holes.
The West Side Market he mentioned is really cool. You can grab gyros and climb up above the alcove and people watch while you eat. That's in Ohio City and also tons of great options (Bakersfield has amazing margaritas) and Tremont next door is another fun place to explore. If the weather is good, you can grab the hourly bikes around those neighborhoods and take the towpath all around. https://www.bikecleveland.org/
As for Progressive Field, it's amazing. The bull pens are glass and you can stand right behind the catcher and practically feel the heat coming your way. The food is great and much of it is divided by cleveland "neighborhoods" so you can sample some of our local best. There's a beer wall past the Corner and if craft beer is your thing, you'll be one happy fan. Heritage park out past center field is cool. Also, on a separate note, League Park (a ten minute drive from downtown) has a cool baseball museum and it's where Babe Ruth hit his 500th home run. I believe the museum is only open on Saturdays. http://www.leaguepark.info/
Lots to do in the Land and late September should hopefully be a great fall weekend to explore - have a great trip!