Welcome to the area. There’s plenty of riding to be had in the DC area… some close in, some farther out. Check the “Where to Ride” link on this web page. The ride calendar is also a good place to look.
Scott Adams and Martin Fernandez have a great book about mountain biking in the DC Area: “Mountain Biking the Washington DC/Baltimore Area”. Its in its 4th edition and has plenty of good rides. Scott Adams also has the “Mountain Biking Virginia” book that covers the whole state. Both are well worth the money and can be purchased at your local book store or from Amazon.com.
There is plenty of road riding in the area. Many people are better sources for info than I am on that. I haven’t ridden a road bike for years.
The riding in this area is fine for a hardtail or FS bike. I use both, though I ride the FS more often. My bike of choice would be an XC FS bike with 3-4″ of travel and something that doesn’t bob around too much (no offense intended to anyone named Bob or Robert). I’m building a 6″ travel bike for some of the rougher areas and for when I travel to Colorado, but it won’t be my every-day ride. I ride the hardtail once per week or so in order to keep my bike handling skills sharp.
Hope that helps.