The Atlas Performing Arts Center is located in an historically-Black neighborhood that has had its share of troubles since the riots of the 1960s. While the neighborhood is starting to experience welcome gentrification with the opening of the Atlas in a former movie theater and the opening of several nearby restaurnts, I'm not convinced that it's yet safe to freely walk around in, particularly at night.
The hotels on New York Avenue have a bad reputation. Some of them have been used as welfare hotels, others for various illegal activties such as prostitution. Although I have no personal familiarity with the Howard Johnson Express, I just checked out the Trip Advisor website and found that of 17 posted reviews, ALL were negative--some extremely so! According to the reviews, it's not at all a safe place to stay, particularly for an unaccompanied woman. Please look at the reviews--the URL is below.
My suggestion is that if low price is your objective, that you stay at one of the motels/hotels in the close in suburbs, such as in Arlington, Alexandria, or Falls Church, Virginia. If you'll have a car with you, the exact location won't matter.