There is practically a restaurant, or five, on every block in the District, each one presenting a wide variety of options to choose from. Depending on what neighborhood you are in, you could eat cuisine and experience the culinary culture of 10 different countries, all without leaving a single block! A few good examples of some of these spots would be the U Street neighborhood, Adams Morgan, Georgetown, and Dupont Circle, among others. When you take into consideration the typical student's budget, the more viable restaurants would be in U Street and Adams Morgan, which not only hold the advantage of being but a few blocks away from the campus, but are also kinder to your wallet, as opposed to the pricier Georgetown restaurants. Also, the closer to the campus a restaurant is, the more likely it is to be open late.
There are many options that are great for eating on the move, but for those times that you want to have a three-course meal at a nice sit-down restaurant, some good places include Buca di Beppo. The bottom line is: You'll have opportunities to try new types of cuisine, but there's an excellent chance that in DC you will be able to find anything you're craving, all within a reasonable range of prices.