Beyond NYC, I don't think there are too many, depending on your definition of "major". Albany, NY, comes to mind- it's not a "major" city but it is NY's state capital, which makes it worth a visit IMO. I used to spend a lot of time there and it's a neat little city. The New York State Museum is very good, with lots of exhibits, and there are guided tours of the Capitol. The downtown area's nice, with shops and lots of places to eat. It's also a pretty easy ride up I-87. Hartford, CT, is not too far from Poughkeepsie either, though I've never been there.
