Help Planning NYC trip

Hey guys! I am attempting to take me and my girlfriend on a trip in early April of next year to NYC. I currently live in Huntsville, Alabama but am able to fly free so Travel costs will not be a factor =) I chose early April because there should still be basketball games being played and I would like to go to a game, do not worry or mention ticket prices to ANY types of games, Only mention sports if you believe another season would be more enjoyable (winter, summer, fall, spring).

Have fun! I have no idea what I would do up there and since I am sure some of you either live close or have already been, you guys can pitch me some ideas!

Here is what I am looking for and my limits.

1. $5,000 USD limit. But if it is necessary it can be more.

2. Flight and any major sporting event will not count towards the total budget.

LOOKING FOR

1. Restaurants that I must eat at.
a. Fancy, Fun, Cultural.

2. Points of interest
a. Ground Zero, Statue of Liberty, any museums.

3. Hotels
a. Mainly where I can get a great view of the city and one in a nice location

4. Other fun things and stuff that I have to do if I visit New York.