Mambwe,
I live downtown and whenever I am asked this I always suggest, if you want to do a manageable number of monuments, do the Vietnam Wall, Lincoln Memorial, WWII and Washington Monument. The are all an easy walk on the Mall and represent a little bit of everything. I would recommend the Lincoln and Vietnam Wall at night, if you can, as they take on an entirely different effect, particularly the Wall. The White House is close as well, although pretty boring if you ask me.
The Smithsonian and Capitol Hill could be added as you simply continue on the Mall, however, Arlington Cemetary is across in VA, so that brings time into play. I personally would stay on/around the mall. Grab a map and just figure it out as you go. Most of the museums are pretty easy to get into and free and you are early enough that the tourists/school trips aren't in full swing yet.
If you want to go to a museum I would recommend the Holocaust museum. I'll warn you though, it is VERY intense. However, it is probably one of the most moving experiences/museums (Anne Frank House in the same light) I have ever been to, DC or otherwise.
If you do go to Capitol Hill and want to check out a local wine shop, go to Schneiders of Capitol Hill. Great place with a great selection. It's real close to Union Station (Metro stop there and restaurants as well.)
As for hotels, the two you listed are fine. I would stay in NW to be close to the sights. Just about anyone downtown is going to treat you well and you won't be too far from the sights. The Mayflower is also very nice.
Use Metro when you can as it is run very well and can get you just about anywhere.
Have fun, drop me a line if you want anymore information or local tips/knowledge.
