Okay, that helps me out.
First, do yourself a favor and buy yourself a Metro day pass when you get here, if you don't have any other means of transportation. Only $5, and you get unlimited use of MetroRail from 9:30 am all day long. That's really helpful, for both tourists and residents alike, and I think it'd help you out a lot, since you're probably going to a lot of places with Metro access (ie, National Airport, Smithsonian, Arlington Cemetary, etc. If you need any help finding the closest Metro stop to particular places in the area, let me know.
Since you're into trains and shopping, I would suggest stopping into Union Station. It's hard to do much spotting of trains there unless you walk a few blocks around the perimeter of the station (it's a pretty large yard). The main attraction in Union Station is its beautifully restored turn-of-the-century architecture, as well as the many upscale shops and restaurants they've placed in there. But be sure to watch yourself if you go more than a couple of blocks north and east of the station, since you begin to get into rough areas beyond those points. Fortunately, those areas will be developed over soon, but for now, they're still shady.
One good place to shop that's on a Metro line is the Fashion Center at Pentagon City in Arlington, VA. It's got three full levels of shopping plus a smaller, fourth one for the food court, and lots of upscale shops.
Another good place is Georgetown, as some people have mentioned, both for shopping and clubbing. Georgetown shops are generally either upscale or moderate, and I know that there was a very nice comic book store there with a good deal of anime and manga about 3-5 years ago. Don't know if it's still there. Also, the clubs in Georgetown tend to be a bit on the classy side--it is the home of the famous Blues Alley, after all, so you'll see quite a few jazz clubs over there. If you're more into hard rock and dance stuff, you'll want to go towards Adams-Morgan in central DC, where a lot of the young 20s crowd hangs out. There, among others, you'll find the 9:30 Club, which is probably the most well-known local rock club is--it often serves as a smaller venue for the middle-tier rock groups. Crime tends to be high around there, though, so if you go, watch your back.
Old Town Alexandria is excellent for plane spotting, if you're going to do that, because the planes flying into DCA fly almost parallel to the Alexandria shore. There's a park on the waterfront there where you can kick back, relax and watch the planes land. It's also arguably just as good at Gravelly Point because, although the aircraft aren't landing/taking off right over your head, it's much easier to get to because there's a Metro station fairly nearby, you get to see just as many planes as with the north approach, and no airport security people or police are going to be watching you/hassling you. So it's more convenient. In contrast, unless you're willing to do some major dodging of cars, there's really no way to get from the Nat'l Airport Metro to Gravelly Point. Unless you have a car at your disposal, of course.
As for museums, I would suggest going to the Air & Space (definitely), American History and Natural History. The Archives is a nice place, too. Unless you're into art, I'd recommend staying away from the Corcoran, the Nat'l Gallery, etc., since these places are often likely to put people to sleep. The Holocaust Museum is supposed to be powerfully moving, or so I've been told, but I've never been. Also of interest is the Newseum in Rosslyn (just across the river in Arlington, VA), a museum for the news media, which is highly recommended--go before they close it, as they're shutting down soon and won't reopen until 2005 (they'r moving into a place in DC). Finally, don't forget the National Geographic Museum if you're into science--compared to the Smithsonians, there's not an overwhelming amount of stuff there, but there's always some main exhibit open there.
Just a short mention of neighborhoods and crime--if you're going to be roaming around the area, know that almost all places on the Virginia side of the river are to be considered pretty safe. There are a few shady areas in Arlington, Alexandria, etc., but no widespread areas where you're likely to get hassled. Maryland is less so, but still more safe than DC--for example, most places in Montgomery County are decently safe, but PG county is a bit shady in a lot of places close to DC. But on to DC itself. My suggestions are these: 1.) NW DC is mostly safe--Georgetown and Foggy Bottom (around GWU) are pretty safe places. SW DC is okay. The hot spots of crime, though, are NE and *especially* SE DC. 2.) Don't go north or east of Union Station at night. 3.) Don't go north of Mt. Vernon Square at night. 4.) Anything significantly east of the Capitol, unless you're going to RFK Stadium or the Armory, is right out whether in daylight or not. 5.) Don't cross the Anacostia River. There's nothing much to see over there, and some really *bad* neighborhoods. 6.) Stay in the tourist areas (ie, the Mall), and you'll be fine. 7.) Watch your back after dark, no matter what area you're in--I always do, even after having lived here for 20+ years. Beyond that, common sense applies--although, I'm guessing that as a New Yorker, you'll do fine in staying safe here.
If there's anything else you want to know, just ask and I'll try to answer! Have fun down here when you get in!