Just for the people who were thinking about neighborhoods -- don't count out places like Logan Square, U Street, and Columbia Heights. They've undergone a tremendous turnaround in the last 5 years or so -- super-safe (for the single girls from New England that were worrying -- I'm one of those too!), closer to downtown and the Capitol than anything on Connecticut Ave (at least Logan Square and U Street are), and I would say have more character too -- and most importantly, are cheaper than your Woodley/Cleveland Park options. Once you get too far up Connecticut, you either get a family atmosphere -- or if you go really far up, lots of AU students.
Another neighborhood, for people not put off by a place that is still arguably in transition but seems pretty safe, is LeDroit Park. It's on Florida in NW, near Howard U, and getting super spruced-up. Cheaper rents, and the 96 bus (which goes straight to the Capitol) is right there.
Also, Eastern Market area is REALLY nice. Don't be put off by the fact that the street addresses say SE -- Southeast doesn't start to feel unsafe until you're south of the highway. And it's quite close to the Capitol.