VA options
Hi Jay:
I used to live in VA, so I am more familiar with the airports there. Leesburg is a nice airport, but it's a hike into DC. I am guessing that 267 to 66 is the fastest way in, but that will take about an hour. Hopefully someone who still lives there can give you a better estimate of the time.
Judging from mapquest Gaithesburg, MD is a good option as Mike pointed out. The metro is a great way to get around DC. It's clean, safe, quiet and inexpensive.
If you are an AOPA member take a look at their ADIZ penetration animated presentation. It's pretty good.
Also, be very sure you know where Camp David is. It should be delineated on your GPS.
Have a good trip, and be careful.
Antony