The advice above is great. Not too much to add there. Bringing your own chow is a good idea, just make sure you check to see the bring-in bag size limitations, they are enforced. Bring an extra layer and sunscreen. We went last year with night session tickets and saw Federer-Blake, Shaughnessy-Clijsters on Ashe. Awesome Fed-Blake match, incredible Davis Cup atmosphere for key games of the match. Because it was a night session ticket, we were only let in at the time on the ticket, not before, but we were free to roam around the outer courts. Great play going on there, you are right up close, and a massive jumbotron shows ongoing matches (we caught the fantastic Philipoussis-Nalabandian match still going on from the day session on Armstrong). Bonus was watching McEnroe play a practice match.
Staying in the city is a good idea, NYC is plenty of fun, and won't break the bank if you know where to go. Think the funpass price has gone up to $7 but it's still a good deal for a day in the city, though for more than one day, the weekly metrocard may be better.
check out this link:
Steve F. - 09:51am Jul 20, 2003 PST (#2 of 7)
Get a metrocard "Funpass" it will cost $4 for each day, but you get unlimited rides on the train for that day. If you stay more than three days, get a weekly unlimited ride metrocard, that'll set you back $17 I think, but will save you the hassle of buying a funpass everyday.
check out the subway system map at: http://www.mta.nyc.ny.us/nyct/maps/submap.htm
The purple line that extends out to the right is the #7 train, and the last stop is Flushing, Queens where the USTA Tennis Center is. If you see where the #7 train starts it's 42nd Street, the heart of midtown Manhattan. So any hotel right there near 42nd Street would be a good choice, but pricey. The train takes about hmm, 40 minutes? I can't recall for sure.
Include time to hit a couple restaurants in the city, but not in Times Square because it's not really NYC, it's only the tourist hub. There are great places to eat everywhere in great neighborhoods all over town, check out this link to the Zagat guide for ideas:
Good luck and have fun.