If your child already enjoys the American Girl dolls, then she'll likely enjoy the store. I've been to the AG store in Chicago (had the afternoon tea) and the AG store in Los Angeles (saw a program with skaters Kristi Yamaguchi and Marai Nagasu) and both were enjoyable. But yes, AG and all of their activities can be expensive. Part of the fun is to bring the doll along for the ride, so if you're planning on walking about the town, that's an extra thing to trek along with you.
My daughter was 4 1/2 when we went to NYC and the AG store wasn't yet open when we went. She and her brother (7 at the time) enjoyed the Statue of Liberty (tho the interior was closed since we were there less than a year after 9/11) and the boat ride over. Neither kid really enjoyed Ellis Island, but I think they'd have liked it if they were a bit older. Particularly interesting is the display of items submitted by descendants of Ellis Island passengers. An older child might also enjoy the computers where they can find an ancestor's name that traveled through Ellis Island. You may want to confirm that they were passengers through there ahead of time to help your child navigate the system. The Stephen P. Morse database (free online) is a good place to do that.
Younger kids will enjoy the Merry-Go-Round at Central Park. That's one speedy Merry-Go-Round! The Empire State Building is great. If you plan to go there, I highly recommend that you purchase your tickets online ahead of time as it'll save you a good amount of time once you get there. The information will be on their website. A hotdog from a street vender is a fun and inexpensive way to feed yourself one of your meals. Another option is NY Pizza - Grimaldi's in Brooklyn is rated #1 by Zagats. You take the subway under the East River to get there, which is fascinating for the kids.
When we went, we stayed in town at a place called Plaza 50, which has now been remodeled and renamed Affinia 50. It's a convenient location, close to subway stops. We got GREAT rates at that time, about $150 a night for a suite with a full kitchen. I don't know if you can still get those kinds of rates, but it was really handy with kids (and less expensive) to make our own breakfast and one other meal of the day. There was a grocery store really close and the BEST bagels in the world were right around the corner. I still drool thinking about Ess-a-bagel! I've been known to bribe friends to bring some back with them!
Sounds like a fun trip! I hope you have a great time!