I went to the US Open twice - you can buy tickets on-line or from ticket sellers. I personally like to go to the early days of the tournament as you get to see more tennis and tennis players. Plus the costs are much more amenable - you get the same feel of being there, but at a better price. When I was at the US Open I met a man who would take vacation every year and buy tickets for the first week. He really enjoyed it.
You can take public transportation into the tennis area, so worrying about your own transportation is not an issue. That way you can get yourself the type of hotel you might like better or afford better - plus you could see other areas of New York. The tournament itself is actually held on Long Island (as I remember) - so you could even stay out there and not in Manhattan (possible price break on a hotel).
The food at the tournament as well as T-shirts, etc, is like being at a concert - expensive and yet unique to that particular year of the tournament in the case of the souvenirs. One thing about going in the first days is you get to see tennis play on the outer courts and it is a much more intimate experience - it also shows you how good these guys really are - I remember watching Michael Chang at the French Open and he was only about 50 feet from me - amazing how he scampered around and hit the ball. The perspective is nothing like that which the TV can give.
I've also been to Wimbledon and the French Open - the opening day of each. At Wimbledon I queued up and was able to get in the grounds. At the French Open, I bought tickets from a couple selling theirs for the grand stadium at a 10Euro premium above what they paid. At Wimbledon I had strawberries and cream (traditional) and at the French Open Crepes Suzette and some awesome mushrooms - the crepes being the tradition in France. At the US Open it would be more US type food - hot dogs, hamburgers - steaks...etc.
My husband and I love watching the tennis tournaments and for me, I still need to see the Australian Open to meet my goal of seeing all the Grand Slams in person - just one more to go!