Hey Catherine,
I lived in VA for about 20 years. My suggestion would be to fly into Regan Internation Airport. Another option is to fly into Dullas, but it's maybe a 30 minute taxi ride to get close to DC from there and depending on the time of day (avoid rush hour) it could take hours.
You can stay in Rosslyn, or DC. Use the Metro Rail to get around. It's clean, and takes you just about anywhere you want to go including a station at Arlington Cemetery. If you do fly into Dullas, you could stay closer to the airport like in Vienna, or Falls church. I'm not sure how close the hotels are to the stations, so if you do go that route, make sure you ask about getting to a station unless you do decide to rent a car. Parking however at the outlaying stations was non-existant if you were not there by 6:00AM. The Suburbs of VA are generally nice, but your not downtown, and traffic is a nightmare during rush hour to get downtown. I'd recommend staying in the city.
HERE is a map of the metro. As you can see it is quite extensive. If you flyinto Regan there is a metro station there, or you can take a cab or shuttle from the airport to the hotel. I would think any major hotel in DC or Rosslyn is going to provide that as a service.
There are a ton of hotels in Washington, so just pick a major name (Hilton, Marriott, whatever), and it will be there. Rosslyn is across the river, but right on the metro line, and VERY close to Arlington Cemetery. If you want, I can do a bit more research and even suggest some hotels, but I think you should not have issues, just make sure the the hotel is near a station.
The metro also has stops at/near the Capital, Vietnam Memorial, Lincoln Memorial, the Mall, Smithsonian and anywhere else you may want to visit in Washington. I have not been back there for 12 year, but the traffic sucked then, parking was a nightmare, and I hear it is even worst now, so getting a car is actually more trouble than it's worth unless you need to visit area's outside the city like Gettysburg.
Again, sorry for your loss, and if you have questions about DC, or VA, PM me as you wish.