Okay I know the hotel. I have had a few drinks in hotel bar prior to hockey games at Madison Square Garden which is acroos the street from your hotel. I grew up less than a mile from your hotel. In terms of places to eat I will give you few of my favorites.
Mexican- there are 2 places I go for Mexican, the first is Maryanns which is on the corner of 16th street and 8th avenue and the the other is Tequilas which is on 23rd street just east of 9th avenue. Both places have good food and great drinks for decent prices.
Chinese. My favorite is Grand Sichuan(? spelling) it is on the corner of 24th street and 9th avenue. It has great food decent prices the service is so so but the food is so good that I dont mind the so so service. The 2nd place is The Ginger House which is on 7th avenue between 28th and 29 th street. Just 2 blocks south of your hotel.
Pizza= By far my favorit pizza is John's pizza, there are 3 locations in the city. The closest one to you is in the times square area. It is on 44th street between 8th avenue and Broadway. If you like sausage get a pie with sausage. If you are in the village and want a good slice of pizza there is a place called joe's on 6th avenue just north of Bleecker street- great slice.
Italian- Carmines is great and their portions are big enough for 3-4 people. There are 2 carmines one is on 44th street and Broadway(very touristy-long lines) the other is on Broadway and 90th street,this is the one we go to. Another Italian place we go to is Andreas which is on 3rd avenue and 23rd street.
Burgers-The Shake Shack in Madison Park is very popular. The lines are crazy long but worth the wait. The park is at 23rd street and 5th avenue. Another great burger is in the Corner Bistro which is on west 4th street and 8th avenue
Spanish food- If you like Paella there is a restaurant called El Quijote which is right next to the Chelsea Hotel 23rd street 7th-8th avenue.
If there is anything else that you are interested in eating let me know and I will give you my suggestions.