I did Yankee Stadium and Cooperstown in summer 2003 on a budget. I didn't fly open jaw as you are planning on doing. I flew into JFK, stayed in NYC for a few days and then drove up to Cooperstown.

Before heading to Cooperstown, I went to West Point as well as the FDR Birthplace/Library and Vanderbilt Mansion in Hyde Park, NY. I stayed at a flea-bag Econo Lodge in Poughkeepsie while in the mid-Hudson area.

I'm very frugal so I stayed in Albany at a Howard Johnson and just drove into Cooperstown to spend a day and one full day is all you really need. IIRC, Albany is less than 90 minutes away from Cooperstown and it is a scenic/pleasant drive for most of it. There are also a lot of cheap hotels/motels in Albany and in neighboring Colonie, NY. Cooperstown also has several other museums including a farmer's museum and the Fenimore Art Museum. I only went to the HOF. If you're interested in seeing the other museums (which I've heard are nice), Cooperstown is probably worth more than one day.

As for NYC, I can't really recommend any hotels. I ended up staying at the Hotel Pennsylvania, across from MSG and Herald Sq. for $85/night. It has some very bad reviews online; however, I didn't think it was really that bad but I don't think it was nice enough to recommend.

You're itinerary looks very doable. And I don't think it matters if you go to Yankee Stadium during the day or at night. I'd avoid the bleachers there all together. The LF bleachers, because they're too far from the action. Neither bleacher section allows access to the rest of the stadium; both are blocked off from the rest of the stadium. Also if you're in the bleachers you won't have access to Monument Park before the game (which is worth seeing.)

I hope this helped a little...

I stayed at the Hampton Inn Seaport which was quite nice, quiet, good bed, safe area, and I got a very good rate (for Manhattan) of $150 or so. It isn't a very convenient location for most things, being fairly far from the subway, but I was going to a music festival in Chinatown so it was. I had nice meals at Momofuku and Ramen Setagaya and bought beautiful cheap clothes at Uniqlo .

is the best at securing a quality 3 star hotel.

area. We always stay at the Sofitel. It's gotten more expensive lately so this summer we are trying a cheaper hotel since we are paying for 3 rooms (taking our 3 daughters and son-in-law) and so we are trying the Amsterdam Court. Hope it isn't a dive.