My two cents:

I think the kids will like the ferry ride and the views. Do that early in the morning. You won't have to run at the Staten Island end (you have to go out and then go back in), but don't dawdle or you'll miss the next boat. Then head up to FAO Schwartz/Central Park, where you have more control over how long to spend and can adjust as necessary.

I think a hotel in the vicinity of Central PArk would work best. You can hop onto the subway to get to the ferry and then when you're back you're close to your luggage.