I am way late on posting and asking for suggestions. Basically asking for any can't misses around or in these parks or any can't miss foods. Will be self, wife and two late teenagers.
In order:

Lexington, KY for bourbon (not baseball but what the heck)

• Old Pepper Distillery and Buffalo Trace Distillery (spent way too much money for my "souvenirs"

Cincinnati

• Great ballpark on the river in downtown.
• Ate ballpark food (hotdogs, peanuts, popcorn, helmet sundaes, and I had a nice craft beer)
• Took pictures of the kids with the Joe Morgan, Pete Rose, and Johnny Bench statues. Explained each of them, including that trading Joe Morgan was the worst trade in the history of the Houston Astros as well as the reasoning for the gambling ban on Pete Rose.
• Played the Yankees. Future HoF Aaron Judge hit a monster HR, Elly De La Cruz hit a triple and an HR, and the Yankees lost. So couldn't have drawn it up much better!

Cleveland

• Crummy area of downtown and really nothing special about the ballpark. Closest thing I can relate it to is Guaranteed Rate Field in Chicago.
• Nothing special about the food we encountered, and it was so hot and humid the players acted like they wanted to be there as much as the fans. "Blah" is a nice way to put it.
• Did get pics with the Jim Thome and Bob Feller statues and Satchel Paige plaque so got to give the history lessons on them.
• If every place was great, then we wouldn't appreciate great. So Cleveland does serve a purpose.

Cooperstown
Yankees
Mets
Philadelphia

We have previously hit Washington, Baltimore and Pittsburgh so skipping them this trip.

Have fun!

I went on a number of trips like this when I was a kid and in college....keep score and then look over your score book in 15 years and see how many Hall of Famers you saw without even realizing it at the time.

Enjoy!

OP username checks out!

Kidding aside, that sounds like an awesome vacation!

Cincinnati - Moerlein Lager House, right across the street from the ballpark, good food and beer, views of the river and Roebling Bridge

Cooperstown - Ommegang Brewery, it's a bit outside of town, but it's a small town. Cool facility and they brew a wide variety of beers, including a really good Belgian style triple ale.

For transportation purposes, Cooperstown can be difficult to find a parking spot. But, they have a bus system where you can park in a particular lot and it drops off at the HOF. Also, everything is there within walking distance (except maybe the brewery that was mentioned earlier) so you can park and ride and it's pretty inexpensive.

Thanks everyone for the suggestions so far. I will edit my original post as we go along.

We did the Louisville Slugger Museum and tour last summer, as well as a minor league game there, on our way to Indianapolis for a conference.

Not going to stay the night in Cooperstown, so unsure if we will be able to hit the brewery. Appreciate the parking and bus tips! Staying in Oneonta night before so early day at the Hall of Fame before we drive down to NYC.