On evenings and weekends the Supreme Court parking lot (3rd and A Street NE) is available to the public. Monday-Saturday, meters are generally for two hours until 8pm. On other side streets, there is free two-hour parking. On Sundays there is free street parking.
The number 97 and 96 buses stop on East Capitol. The number 32, 34, 36 and Circulator buses stop two blocks south. The closest Metro is Capitol South (Blue/Orange), about a four-block walk. Union Station (Red) is a 15-minute walk.