I'll confirm G street is good.
Founding Farmers in the trendy place and open for breakfast: http://www.wearefoundingfarmers.com/
Breadline has nice omelets and decent space: http://www.breadline.com/
Corner Bakery has a decent sitting area.
The Met Cafe has lots of options and plenty of seating: http://www.metcafedc.com/main.html
Fast food options of Roti (limited menu), Cosi, Potbelly's, Subway, and Brown Bag Cafe all have places to sit.
1924 Pennsylvania Ave. NW, Washington, DC 20006
The Brown Bag
1099 14th St NW Frnt 1, Washington, DC 20005