From DCA to Friendship Heights, take the Yellow line to Gallery Place/Chinatown (Direction: Mt. Vernon) and once there, switch to the Red (Direction: Shady Grove) and you should be in Friendship Heights soon enough.

The downside to cabs: traffic. DC-area traffic is horrible, and the 14th street bridge is especially bad. Wisconsin Ave. won't be fun most times, either. Also, just so you're prepared, DC cabs have no meters, (zones) and come in an array of colors.

As a former DC-area resident, I'd have to say you'll be fine taking the Metro for most transportation, but I'd also suggest taking a cab back to the hotel at night.

Have fun in DC.