2 nights? Do E 4th non baseball night.
@Galileo did the open container law ever get put in place? If so don't worry about getting a reservation anywhere. Put your name in then just wander bar to bar until you have a table. They are all great, but if you're into that sort of thing I recommend the pig head at Greenhouse. If I had to name one thing at one place.
Baseball night pre game at the Clevelander. Go to the bars in Ohio City after. Cheap uber away. I like Town Hall more than Market Garden, but they're both great. If the night gets late be sure to finish at Bar Cento and stuff your face with the duck fat fries. If you're into smaller bars then do Tremont instead of Ohio City. Too many to name, but South Side and Flying Monkey are our favorites.
Slymans is a must. If you can't get there for lunch go before the baseball game.
Oh, and be sure to take advantage of our non 100 degree weather and enjoy some lake breeze runs while you're (hungoverly) here.