Honestly, baseball is probably the last thing I want to think about right now, given that my Cubs just finished the season with 101 excruciating losses. But if you still enjoy the crack of the bat against the ball, Boomtime Baseball (free) might work for you. While it has some issues, it will at least provide you with that great feeling of knocking baseballs around in a classic era.
Unfortunately, Boomtime Baseball doesn't go for the whole game: It's a series of minigames, most of which just involve you hitting pitches. But the hitting mechanic is rather fun. You swipe down the screen to power up and aim, and then let go to swing hit when the ball comes through. It doesn't really feel much like baseball -- it's more like an arcade game that's themed in baseball memories. But it is fun, and there are a few different types of games to play, including one where you fill up a slugger meter, and another where you bet in "Al's Casino."
I have two gripes with Boomtime Baseball. First, the in-app purchases are frustrating. You need to buy everything in the game, and while that's doable just by earning points in the minigames, the game doesn't let you forget at all that you should be spending money on it.
Also, the presentation is lacking. You'd think that "Boomtime Baseball" would offer up some official information on old players or teams, but nope. All of the players are just generic. And the game's sounds will probably need to be turned off as well. I could only take so many "oh my"s from the old-timey announcer.
All in all, Boomtime Baseball isn't bad, but it's probably only worth picking up if you just really, really need to scratch that ballpark itch now that the real ones are closing up. It's too bad the developers here didn't go further with what started out as an interesting idea.