I've always found Priceline's Name Your Own Price to be very reliable for traveling on a budget. As long as you end up within walking distance of a DC Metro stop you won't have any trouble getting to and from the ballpark and there's so much non-baseball stuff to do in Washington, you don't want to spend your trip eating Papa John's pizza with a case of Budweiser chilling in a tub full of ice water in some Holiday Inn Express in suburban Virginia.
2015 Obligatory Attendance/Record Tracker
LAST GAME: May 22 - Sox 3, Twins 2
NEXT GAME: June 8 - Sox vs. Astros