I echo Will Wilson's post.
Grounds passes are great, free tennis all week the previous week, and AA Stadium absolutely stinks unless you're the 1%.
Get the Waffle Fries.
There's a Holiday Inn within walking distance, but there's no sightseeing in the vicinity. If it's your first trip to NYC- stay in Manhattan, and take the #7 train in. Crowded, though.
If you're a USTA member, check to see when Member Appreciation Day is. They have a nice little event that day- picture taking with the trophy, etc.