I second Bellearye in the east Catskills, over the other two. I think the area that's closest to NYC may be in NJ, though, Mountain Creek. If you can do it, I'd recommend going out to Plattekill, which is ~3 hours away from NYC. It's only open on weekends, though.
In the DC area, the closest is Whitetail, in PA. It's about 1.5 hours away from the city. I get bored of the area after about 4 hours. There's also its sister hill, Roundtop, but I've never been there. It's 2.5 hours from DC, and smaller. Lots of times when people say they're going to DC, they're really not in the city, so you may be closer or farther away, depending. Those are basically your only options less than a 3-hour drive away.
For a really long day trip, I recommend either Timberline or Canaan Valley, in WV. They're in the same valley, 3.5 hours each way from DC, but I've done it as a day trip.
I don't want to be a downer, but if I were going to be in the DC-area for only a few days, I'm not sure checking out the slopes would be how I'd spend them unless there's snowfall like there was last year.
Also, be mindful of the MLK holiday, if that's when you're there. Lots of crowds on weekends, especially school holidays.