Go to National Mall, you will get most of the place that you need to visit like White HOuse, Monument, World War 2nd memorial , linkon memorial and many others different museum.

 There was an extensive threat on this subject a month or two ago.  You might want to search for that.  Lot of good folks gave detailed information.

Hi Ek
There are different tour buses as well. I donot know the exact price for riding these bus may be around 20-25 dollar for each and you can ride  these for two days. That is the best option as they will tour you whole DC. I have no idea about the hotels. Regarding expense, you do not need to pay even a single penny to visit different location in DC except one or two museum.  Regarding transportation you donot need to worry, there are lots of public buses, trains and taxi.
Enjoy DC

You can cover all spots in DC in one day.

What you need:
1. Sun screen cream
2. Sun glasses
3. Water Bottle
4. DC map
5. Camera
6. Bycycle (nice to have ;)

Go early morning on Sunday before 9 am for easy parking and less rush. Park your vehicle at Constitution Avenue (near Washington Monument tower).  

Walk (or cycle) this way:
Start at  Washington Monument tower --> (walk west) US Gov Park (WWII memorial park) ----> (walk west) Lincoln Memorial ---> Walk North West (White House) ---> Walk South West ----> Capitol Hill Building ----> Walk East and there are few museums in that way (musiums are in between constitution Ave and Independece Ave) .. you may visit few of them e.g. National Museum of American History  and another one-  National Museum of Natural History (entry free both). You may also like to visit Air and Space Museum. And walk east, you will arrive to your parking spot ;)

Get a DC map and mark the spots you want to visit and make plan - it saves time. There are few skyscrappers in DC, and unlike NY, all these spots are scattered around open parks .. so easy to navigate and walk around.. enjoy the trip.

thanks, Riten, dinesh 110 and ANS for your valuable input.