First, how long will you be in the city? You mentioned a number of attractions that are all on opposing sides of the City (the Met is on the Upper East Side, the Museum of Natural History is on the Upper West Side, the Broadway shows are right near your hotel in Times Square, Ellis Island will require a trip all the way downtown to Battery Park, and Carrie's apartment is in the Village).
You can do it all, but you will need a fairly tight iternary...especially if you want to devote a few hours to the absolutely fabulous museums you mentioned. For example, to get to Ellis Island, explore, and get back on the ferry will be a few hours, if you don't get stuck in a horrendous line.
One of my favorite things with out of town guests is start in downtown in Battery Park, see the Statue of Liberty (go on the ferry, if the guests would like), walk up the financial district and see the more contemporary architecture contrasted with the architecture of city hall, head up to tribeca and then chinatown (a fantastic neighborhood for visitors to stop in), and then soho for shopping. From Soho, you can walk up to the Village (where Carrie's apartment is, I believe, as well as Magnolia Bakery - the cupcakes featured on SATC).
A good side diversion from either the Met or the Museum of Natural History involves a stop in Central Park. I love, love, love the calm oasis that is the Park, and it's goregous in the summer (that is, away from the 59th street entrance with the horse carriages and the surrounding smell).
ALSO - if you're dead set on seeing "Wicked", book tickets NOW. The show is almost always sold out, especially on heavy tourist times (read: summer, weekends). It's very, very popular with out of town guests.