Chicago is a great place to visit, but if you're short on time then I'm not sure about DC. It's nice enough to spend a day (and that's all it takes) walking round the major attractions, but the place has this really humdrum feel that you wouldn't expect of a city that size.
If you're looking for another east coast city then Boston's pretty cool, or failing that Philadelphia - both are a reasonable Amtrak or coach ride from NYC.
Also, BTW, I grew up near DC and I disagree with this comment. You could spend whole days just seeing the Smithsonian!!! Plus, you can take a trip just out of the city and go to Mt. Vernon (Washington's home) or rent a car and take an extra couple of days to go down to Virginia to see Monticello (Jefferson's home), Ash Lawn Highlands (Monroe's home), Colonial Williamsburg, Yorktown, Jamestown, and all the plantations. So if you're into history, DO make sure you visit DC and the surrounding areas!!