In a post at U.S. News & World Report, Alexis Grant offers ideas for students who don't yet have an internship for the summer.
You can scroll down on the homepage to see the variety of startups in the District of Columbia area. On the application, you can state specifically what you're looking for and whether you'd accept paid or unpaid internships. (There's also the option "prefer paid.") It's open to graduate students, undergraduate students and even high school students. And the site says there's something for everyone, whether you're interested in working in software development, business or marketing.
It promises special events, the chance to meet local founders and to network in the startup community. It sounds like a heck of an opportunity to put some real-world experience on your resume.