Try to book a hotel before coming so you know that amount ahead of time. The two of you for two nights should be at least $450, more at an elite midtown hotel, less in an outer borough (outside Manhattan). Allow $40 for subways and buses, more if you intend taxis (poor idea, as traffic will waste much of your time). Meals can be cheap ($20/day each of you) or fancy ($150/day each) or anything in between.
You can see the harbor for free by taking a round trip (one hour elapsed time) on the Staten Island ferry. Broadway shows usually must be booked well in advance, any popular show is sold out for months. Tickets start at $75 for remote seats, and go up from there.
Major popular museums include the 9/11 memorial, American Museum of Natural History/Rose Space Center, and Metropolitan Museum of Art. Expect to pay admission at each of around $25/person. Central Park is between AMNH (west side) and MMA (east side). Park is free and has a zoo and the john Lennon Memorial.
China Town is near the ferry and 9/11 memorial and has some good restaurants (try Wo Hop). Times Square is basically a sleazy tourist trap, but does have excellent ethnic restaurants on side streets. Greenwich Village for nightlife