I agree that staying in DCA probably won't work and that Crystal City hotels would be ideal, if you can find one in your budget. If not, take a look at the list of nearby hotels on the DCA website - there are some a bit farther from the airport that run shuttles and may be a little less expensive. There is one place listed called the Americana Motel in Arlington. I see this motel every day on my drive to and from work, and have to say that I always thought it looked a little sketchy - sort of a throwback to the 60s, the kind of place that would rent rooms by the month. But I just took a look at tripadvisor, and it's gotten great reviews!! Recent reviews say that it has a shuttle to DCA, and that the price is around $55-75 a night - may be worth checking out.