I really want to take my sons to New York?

I have been dreaming of visiting New York ever since I was a little kid. Now I have kids of my own and my sons really want to go to New York. The problem is that I don't have the money to do it. I want to start a savings account for the trip. I would like to go for a week. It would be me, my husband and our two sons. We live in St. Louis and would like to fly. We would like to stay in a nice and decent (but not extravagant) hotel and do all of the touristy sightseeing things (Yankee game, Statue of Liberty, Broadway show, shopping, museums, etc.) Can someone please give me a ballpark figure of how much money I will need to do this. I have no clue how much we will need and I want to know how long I will have to save. Thanks so much!