My daughter (11) and I have been to shows at the Kennedy Center and Warner Theater over the past 6 months. For the Kennedy Center we dressed very classy in dresses and heels. We were met with some people dressed in tuxedos and formal gowns, while others were in jeans and sneakers. I went to a show a few weeks later with my mom and sister at the Kennedy Center and the same thing - some were over dressed and some were under dressed.
The Warner Theater was similar. It was a cold December day when we went there so myself, my daughter, and her friend all had on pants and a nice top. We fit in nicely...again, with a mix of over and under dressed.
So with those being two of the top three venues for performances in DC, I'd say you are good in pretty much anything. The most important thing in my opinion is to match the people you are going with. So they should all dress in similar styles. I would always go on the dressier side though.