I've parked at the Ruppert Garage on the 1st base side over the years. Self park, you hold on to your keys - Easy in and out. They'll hit you for $47 or so. There's also a couple of valet garages on 158th right around the corner from Stans and Billy's. A couple $ less than Ruppert but a longer wait to get your car after the game since it's valet and they have your key. Either location gives you easy access back to the Deegan.
I've always pre-paid on-line to reserve a spot for crowded Yankee games. Never had an issue. Of course if you are there real early you can always try to get lucky and find parking on the surrounding streets. I like the sure thing and just reserve a spot up front.
As a reminder to some, remember the Yankees don't control / own the parking lots. The city oversees them.