Very easy with a rental car.  Early next year with the Silver line operating it will be even better.  A taxi from downtown DC or Alexandria would probably be expensive going out and back.  Maybe someone else can give you an exact price.

Cheap and easy would be take the metro to the Falls Church metro stop, and then take a short taxi ride to Tyson's to the hotel you want to get to versus paying for the trip from downtown.  Red Top cab is best IMHO.

If you took a car, I'm guessing the trip would be about $35-$40 each way and town cars are slightly more, but more comfortable.  I'm also guessing you could ask the driver to wait for a small fee and return trip...or schedule the return trip through the service.  There are a lot of good services in the area, look for a group on or living social for a good deal and buy ahead of time.

Depending on the hotel and time, would be very difficult to be discreet.  For example, Westin at Tyson's would be very obvious you're getting dropped off by cab and being picked up an hour later - but whose business is it anyways what you're doing there.  Hilton, for example, is big enough that I think it would go relatively unnoticed.  That being said, either way wouldn't be an issue is my guess, just your comfort level

If you're here regularly maybe use Zip car rental, or rent outside of airport.  Rentals outside of the airport (they have them downtown and other places), its about a 1/2 to sometimes even a 1/3 the price of going to the rental counter at Reagan National Airport.

Along with a map and directions most of them show you normal cab and limo fares from the airports and downtownl.p.

Go here  http://www.taxifarefinder.com/main.php?city=Washington-DC

Aside from myself, , there are many lovely ladies in the Tysons area. Cabs are easy to come by in this area. In fact at times I have needed one and I just use my yellow cab application and they arrive in 15 mins or less. If you are coming or going as long as it is not rush hour traffic, you are good as gold.  So don't let any concerns get in the way of your fun!!

Thx all for the feedback