Look at
www.eqr.com, I live in one of the buildings in DC and love it. They change their prices daily, which is annoying to me. Sometime the price comes down a lot....
Another one is 1499 Mass. It's very close to Thomas Circle. McPherson station is a few blocks away, so is Farragut North (Red line).... Maybe 10 mins walk to DuPont Circle. Lots of apartments near Thomas/Logan circles. The ones don't allow pets (or no large pets) are cheaper in my opinion. Try 1234 Mass or Cambridge. They are on the northern downtown DC. Do a yellow page search for apartment using 12th and L st NW for location. I wouldn't go below 12th street or above N or O st. If you live in the above area, you are very close to K street where lots of bars/lounges are packed with people

Also only 1 to 1.5 miles away from the Mall, and short distance to the white house.
I heard Imperial near Dupont is good... cheaper. I have a big dog so many apartments are out of questions for me.
Try Rent.com as well, you can pick locations (downtown, Dupont, and Penn Qrt). If you sign a lease, you also get $100 from rent.com (I am not advertising for them... I got the $100 card and used on my first food shopping).
Good luck!