I lived at Dorchester Towers for a year for my first apartment, but I didn't realize how much I loved it until I started reading reviews for other D.C. apartments. While it doesn't have a gym, it does have a pool, a beautiful rose garden, and the coolest rooftop area (garden/tables/swings/fountains) that I have ever seen! The roof also has a great view of all of the monuments and the pentagon.
The halls and stairwells are nice and ALWAYS very clean. Plus I never saw a rodent or roach, which would have really freaked me out. I was able to have a cat for no extra charge. I did have a bit of an ant problem, around the cat food, but I never reported it. Though its an older building the only thing I ever had to report was a broken garbage disposal and that was fixed within a day or two.
Overall I really enjoyed my time at Dorchester. The windows were large, the kitchen was huge, and the closet space was plentiful. The only thing that annoyed me about the place was the fact that the elevator was out of commission for 6 months (maybe more since I left) while they fixed it -- this terribly inconvenient. Also, they don't accept packages and the lobby is kind of cheezy 70's looking.
That aside, if I didn't have to live in the city for work I would love to go back!