No advice on the flight, as I was visiting my dad on the East Coast and we drove up.
We spent 5-6 hours at the Museum. Really enjoyed everything there and just spent a good amount of time watching all the videos and reading as much as I could, as I may never make it back.
As for other stuff, Doubleday Field was cool, but didn't spend a ton of time there. There are a ton of little shots in downtown filled with baseball stuff. We spent a couple hours walking around there as well.
The night we were there, we hit up the Cooperstown Dreams Park. It's a huge complex that hosts youth tournaments during the summer. We had heard it was the championship night with fireworks and what not, so stopped in to watch and see the fireworks. It was quite the place.