I've never been, but isn't Horseshoe Curve within a few hours drive of NYC?
http://www.railroadcity.com/visit/world-famous-horseshoe-curve/
And then theres the Strasburg Railroad Museum in Pennsylvania as well.
http://www.rrmuseumpa.org/
and the Strasburg Railroad.
http://www.strasburgrailroad.com/
and you can stay at the Red Caboose Motel while you're in Strasburg exploring Amish Country.
http://www.redcaboosemotel.com/
http://www.padutchcountry.com/index.asp
The B&O Museum is in Baltimore, Maryland and its close enough to the Baltimore Inner Harbor that you can shop and dine at the Inner Harbor (and tour the USS Constellation at the Maritime Museum) before or after your B&O museum visit.
http://baltimore.org/article/baltimore-inner-harbor
While you're in Baltimore, you might want to stop by MB Klein Hobby Shop, a favorite on line model train vendor's store.
http://www.modeltrainstuff.com/
It looks like you'll miss The Great Scale Model Train Show while you're in Baltimore as the winter show is scheduled for Feb 7th and 8th. But if you're still here in February, its worth the visit.
http://www.gsmts.com/index.htm
When visiting DC, the Smithsonian Air and Space Museum is the most popular museum on the Mall in DC. But its worth the trip to the Virginia suburbs to see the Smithsonian Udvar Hazy Air and Space Museum, which has a lot of vehicles too large for the museum in town. The Udvar Hazy Air and Space Museum has a space shuttle, a SR-71 Blackbird, a Concord SST, the Enola Gay, and much more.
http://airandspace.si.edu/visit/udvar-hazy-center/
The only Smithsonian that I believe has trains is the American History Museum on the Mall. Theres also a few cars and trucks on display in the American History Museum, along with other artifacts of American culture and history. The Smithsonian Castle building (the oldest structure on the mall) might also have a steam engine on display, though its been many years since I've been there. Besides the Smithsonian's several museums. The National Zoo in Washington, DC is also worth a visit if that sort of thing is of interest. There are several other museums, besides the Smithsonian museums and galleries in Washington, DC, depending on your interests (Spy Museum, Crime Museum, Holocaust Museum, etc).
Other points of interest within a couple hours drive of Washington, are Gettysburg, Pennsylvania (if American Civil War history interests you) and Skyline Drive in the Shenandoah National Forest starting in Front Royal, Virginia (not far from Virginia's wine country).
Since I mentioned museums for trains, planes and even ships, I figure, I'll also mention the AACA (Antique Auto Club of America) Museum in Harrisburg, Pennsylvania (not far from Baltimore and only a two hour drive from Washington, DC).
http://www.aacamuseum.org/