I agree with franknbeans. There are lots of places like that around here.
Find out exactly where you will be living in (you do NOT want to have to drive across DC or around the Beltway to get to your horse, so you want something on the same side of town as where you're living -- if you're downtown, that'll be tough. You can still find something, but the drive will be less fun).
Will you be able to visit and find a barn before you actually move? If so, schedule visits to a bunch of facilities and see where you feel most comfortable.
Be prepared for a LOT more traffic than you ever saw in Colorado. I'm in Colorado right now, and we were driving up I-25 and my mom was complaining about how horrible the traffic was - a slow down for an accident. We were still moving, but much below the speed limit. That sort of traffic is what I drive in EVERY DAY in Virginia now. So think about that when picking a boarding facility.
It was mentioned earlier that indoor arenas are harder to find. There are some around, but most are a bit farther out (at least on the Virginia side of DC), and quite a bit more expensive.
On the other hand, it's much harder to ride year-round outdoors around here than it is in Colorado. In Colorado I rode almost every day. Here, there's usually a month or two in the winter when the wind is bitter cold and the ground is covered in ice, and a month or two in the summer when it's really hot and humid. 90 degrees and dry in Colorado (like it was yesterday) is NOTHING like 90 degrees and humid in DC. And we even had several days this year with a heat index around 115. So those extremes make riding difficult.
Also, don't know what your situation is now, but one difference that struck me when I moved here is the lack of instructors at the stables. In Colorado it always seemed that a barn was run by an instructor, so they pretty much came together. Here, there are many small barns with no resident instructor (not all - some do have one or more, but there are so many without that it surprised me). That's good and bad - traveling instructors can be difficult to find sometimes, but on the other hand, if you try one and don't like him/her, you can just try a different one next time. If you can trailer-in to lessons, you'll have even more options open to you.
Let's see, other things I've noticed...
You have to watch out for founder more. In Colorado, founder is pretty rare unless a horse breaks into the feed room. In Virginia, horses can easily founder on the spring grass. If you have an "easy keeper" you might need a muzzle part of the year. But of course the other side of that is that you don't need nearly as much hay as in Colorado.
And scratches. I'd never even heard of that in my 22 years in Colorado. It seems most horses around Virginia get it at some point each year. It's little sores on their legs that come from the moisture. There are a wide variety of theories about how to treat it, and no real proven method.
Good luck with the move. If you have any more questions about the area, I'm always happy to help.