Um, I'm not sure where you're talking about, because you can rent a whole townhouse to yourself that is less than a ten minute walk door to door for about $3,500-$4,000 per month. And these almost always come with at least one parking space in the rear. In fact, the townhouse next door to me is for rent right now and has a parking space.
As for an apartment, there are definitely a few above ground apartments that are within walking distance (like on 38th, 39th, S, R or T streets above Reservoir road). I looked at one last June that was a one bedroom for $1350/month. I think the best way to find an apartment is to come here and look in person. Walk around the streets near the school and bring your cellphone to call numbers on the "For Rent" signs.
Parking is a problem because the residents of Georgetown (only area in DC that is like this) voted and decided to make street parking permits only available to DC residents (so your car has to be registered here and you have to get a DC driver's license too). Apparently they did this so that the students wouldn't clog up the streets with their cars.
I, however, love my car and the independence that comes with it (and the ability to go to the grocery store only once a week versus like every other day if you're walking or taking the bus), so I braved the parking here. You can do what I did, which was to get a 6-month street parking permit (it's non-renewable, but any student at a university in DC can buy one, you just have to get a confirmation of enrollment from the registrar's office to take to the DMV) at the DMV for $250, and then rent a private parking space nearby after that (which typically run between $90-150/month).