I’m a member of the Capitol Hill Friends group (http://www.capitolhillfriends.org/). Unlike most of the Quaker meetings in the area, we meet on Sunday afternoons starting at 4. You’d be very welcome!
Also, the website http://www.quakermaps.com/ is a great place to go to find area Quaker meetings in a visual and easy to use format. Each meeting has it’s own flavor and character, so hopefully you kind find something that fits you.