I live there now, in the Logan Circle neighborhood. I know I'm biased, but I really think it's the best area in DC.
I second the Ethiopian food recommendation. Try Etete on 9th St or Lalibela on 14th and P. Get the vegetarian sampler and the doro wat.
As for cheap shopping -- what sort of goods are you looking for?
You can read DCist.com for info on what's going on around town. Washingtonian.com is also good, especially for restaurant recommendations (they put out annual lists of the 100 Best and 100 Best Cheap Eats. So useful). The Washington City Paper is a free weekly paper, and is great for info on weekend and upcoming events.
I'm moving away from DC in a few weeks. I've always said that I'm bored with DC and ready for somehwhere new, but now I find myself getting sentimental about my home for the past 3 years.
On the road of life, do not pause for suicidal chipmunks who freeze in your headlights, seeking death by your tires...