Washington DC is actually pretty big on sports. For football there are lot of Redskins fans, basketballs fans have the Wizards, baseball is the Nationals, and hockey fans (which is VERY popular) have the Capitals. Unfortunately, tickets to these games (minus baseball, usually) can be quite expensive. A cheap hockey ticket is $40 to be up in the nosebleeds.
One often overlooked sport is outdoor soccer, which is the venue for the DC United. You may have to trust me on this, until you go to a game, but outdoor soccer has gotten a bad rep as being really boring. It is actually a really good time! And tickets are not that expensive, and easy to get. DC United plays in RFK stadium (blue and orange lines). The first home game of the season is March 10.
PS. that huge section of chanting fans? They are the Barra Brava, DC United's "12 man".
