The First Street route is great! Straight to the hospital. I hope the OP visits this thread again. I fear she may have gotten discouraged by the first wave of responses. Anyways, First from the Capitol (take a little jog to the right on I/Eye just north of Mass) goes straight up. I usually turn off at RIA, but now I'm adding this route to my repertoire.
To Tina--it took me 52 minutes from Old Town Alexandria to the Hospital complex going up First. I do not ride like a messenger, so I don't blow through stoplights and such. I figure, if you work at a hospital, you're more likely to not blow through stoplights, too. I don't know the mileage because I'm computer-free. In fact, this new route took off about 10 minutes from my overall commute.
From RIA, there is a hill, but it's not bad and the traffic is light and, wow, the air is fresher at the top of that hill! No problems with people, and there appeared to be very little glass. There was more glass on First at Florida NW.
Same Time, if you prefer riding on streets to riding on trails, we can figure out a route from SS. I ride on streets all through DC, and have some good routes to/from Capitol Hill, at least as far as the Reservoir/Hospitals-Brookland and close in Prince Georges.
Thanks for the help. Even if Tina has abandoned all hope, I have a new route!