That's my favorite hotel. There's something about the history of the place that is unbelievably charming. Also, their breakfast buffet is a delight.
I suggest dinner at Becco, which is owned by the Bastianich family. Lidia Bastianich is a TV chef. The food is very good, and the nightly pasta special is the best buy in NY.
If you go to Chinatown, the food at WoHop is ridiculously inexpensive, although it's not authentic, more Chinese-American. You can also visit Little Italy and have a nice pastry outside, but Little Italy is really Chinese now.
If you're downtown, I love the view at the Ritz Carlton Battery Park, so stop and have a drink. My other favorite place was the Rainbow Grill, but it's closed now. So sad.
Apart from the obvious tourist things like the Statue of Liberty, Empire State Building and so on, try and buy tickets to a Broadway show at the discount booth
in Times Square. I would also recommend Sunday brunch on either the World Yacht or the Batueaux.
http://www.bateauxnewyork.com/http://www.worldyacht.com