When you first visited Hopkins, your tour guide told you all about D.C.: "It's close to Hopkins. You'll visit all the time." Your tour guide was lying. Unfortunately, most freshmen never make it down to Washington because they don't have cars, or because they have classes every day and haven't developed the cavalier attitude of a true college student towards lecture attendance. It's a shame, because D.C. isn't that hard to get to, and it's always worth the trip.
If you have a car, take I-95 south to Washington. Depending on your final destination, there are multiple, different routes into the city, so ask someone from the area, use Mapquest.com, or consult an actual map. If you don't have a car, things are trickier. On a weekday, take the free JHMI shuttle to Penn Station, and the MARC train will get you to Union Station in D.C. The trip should take about one hour, although non-peak trains take longer and the MARC isn't known for punctuality.
Once you make it to Union Station, follow the signs to the Metro and hop on the Red Line. The Metro will take you almost everywhere in Washington for a few dollars, is probably the easiest public transit system in the country to use, and features air conditioning. With that in mind, here are a few areas to check out, based on their metro stops.
On the Red Line, your first stop should be Dupont Circle. The best reason to visit Washington has nothing to do with civics or our hallowed halls of government, and everything to do with cheap Mexican food. Once you leave Dupont Circle Metro Station, walk down 19th Street to the alley at 1220, near the Melting Pot restaurant. In the alley, visit the Well Dressed Burrito, which will ruin your perception of Baltimore's Mexican food forever. Its only open a few hours for lunch on weekdays, but you can get an El Gordo burrito platter the size of your face for $5.50.
If you can still move, Connecticut Avenue has a number of other restaurants and stores, and Visions D.C. (1927 Florida Avenue) is a great movie theater that features offbeat movies, food and beer. Finally, if you're feeling down, check out the nationally-televised Compliment Man, who hangs out in front of the Cos' at 1700 Connecticut Avenue. He won't ask for money, and he'll probably have something nice to say.
Adams Morgan and Georgetown are the two best areas for shopping, restaurants, and bars. Adams Morgan, located on 18th Street (the Woodley Park Zoo/Adams Morgan stop on the Red Line), has tons of good ethnic restaurants and more hipster bars than Fells Point. Due to Georgetown residents' deep fear of people who aren't rich, the closest the Metro gets to the area is the Foggy Bottom/GWU stop on the Orange Line.
From here, follow Pennsylvania Avenue for about 10 minutes to M street (this is an epic walk in the summer heat). Georgetown has a large mix of normal chain stores, expensive clothing boutiques, and weird small stores. If your tastes in music run more toward Jonathan Richman than John Mayer, Smash (3285 1/2 M Street) has a good selection of music and appropriately unfriendly music store clerks.
If you're actually interested in cultural activities, the Smithsonian stop on the Orange and Blue Lines will lead you to a huge number of museums, government buildings, and the Washington Monument. Power-hungry IR majors will love the International Spy Museum (800 F Street NW, accessible from the Gallery Place/Chinatown stop on the Red Line). At $13, it's one of the most expensive museums in Washington, but you get to see the real versions of James Bond's toys.
Unfortunately, both the Metro and the MARC stop service early each night. Likewise, if you're planning to see a concert or spend a night in Adams Morgan, you'll have a hard time getting back without driving. I can only tell you to master a vital skill of the college freshman: make friends with someone who has a car.