OK I am DC/MD born and raised.... so here are some important tips safetywise... and a few others.
Metro system is a great way to commute, I myself relied on it heavily. Don't mingle on the metro, about half of the people on the metro during rush hour are tired working people, one fourth are tourists, and the other one fourth tend to be school kids or crazies... be weary of the crazies. Not many people adhere to the elderly/handicapped seating rules (I do but thats because I would want people to do that for me if I had troubles). most people (other then the crazies) will not mingle with you.
Northwest is the best area to be in by far. Avoid parts of Northeast and Southeast unless you carry your own armed guard.
Try to find someone who can go with you in the evenings, DC is a city after all, you'll be alot safer if there are 2 of you. Always be aware of your surroundings. I don't say this stuff to scare you, its just that alot of people come to this city and forget that its a city like many others. There are areas that are great fun and there are areas that are not so safe. Use people who live there to help you out. They are the best resources and can tell you alot. Always ask your seasoned dcers for help/advice... they know the safest areas/streets, etc.
Bethesda is a great place for shopping (not if your on a budget though) and dining(dining is more reasonable).
A great place to eat for lunch is AKA Friscoes or Rocklands on Wisconsin Ave in Georgetown area.
Fresh fields is the best grocer, everything is made fresh and is very healthy and very good. they focus on organic grown products.
Act like you belong and you will... Have fun, be safe, enjoy it!
Good Luck!
Dawn