Hi Leon,
I live in the DC area and would be happy to help! By far and away the best way to get around in downtown DC is a combination of the subway (aka Metro) and walking. Here is a link to the Metro rail system:
http://www.wmata.com/rail/maps/map.cfm?
You can also ride buses are part of this system if you need to go somewhere the Metro doesn't go. There's bus information / schedules on the
www.wmata.com site as well. In general the Metro is well maintained and safe to ride in all directions.
In terms of the city, its broken into four quadrants: NW, SW, NE, SE. The age old wisdom is that NW is the safest part of the district by far. That's where most of the museums, attractions, etc. are located but there are some exceptions. For instance, Nationals Park (where the Nationals play) is in SE and they are completely renovating that area which has improved it significantly. Georgetown is in NW as well. It's a great spot to shop, browse, etc. in downtown.
I personally would suggest you consider staying along the Metro line outside of the city in VA. Clarendon is a nice, hip area that's a few Metro stops outside of the city and located in Arlington County, VA. All of the stops in Arlington are nice and there are hotels.
Not sure what types of activities you want to do while here but a few of my favorites include:
* Iwo Jima memorial / Arlington Cemetery / General Lee's memorial - all are within walking distance of the Rosslyn Metro stop (Orange line)
* Mount Vernon (George Washington's home) - pretty far outside the city but nice. You can either ride the subway and then catch a bus or drive there
* Spy Museum - downtown, interesting stuff if you like gadgets, spy stories, etc.
* Holocaust Museum - downtown, very very good but you need to be prepared for pretty graphic information and to leave extremely depressed. It is phenomenal but not a "happy, happy" place as you can imagine.
* Smithsonian Museum of Natural History - downtown, my favorite of the Smithsonian museums. Massive dinosaurs, etc. everywhere
* Smithsonian Air and Space Museum - downtown, my second favorite. There is also another one near Dulles Airport (30 miles West of DC) that is awesome as well if you want to drive out there
* Try to stop by Ford's Theater and see the exhibit on the Assassination of Lincoln. I believe you can get in and see it regardless of whether the theater is having a show or not but you'll want to check
* Of course you might want to hit the "monuments" as they are called which are all downtown as well: National monument, Jefferson memorial, Lincoln memorial, White House, etc.
I hope this helps and would love to do a meet and greet while you're in the area if you have time.
jeff