I know that I have some readers out there who are very familiar with the Washington DC area - I NEED YOUR HELP!

Chad and I have decided to take an anniversary trip to Washington DC sometime around the end of April/beginning of May (our anniversary is April 26). I won't have a ton of time to google travel tips to my heart's content, so I need you all to tell me what I have to do in DC.
Where should we eat?
What Smithsonians are must-sees?
What time of day is best to do everything?
Any insider tips you have to share?
We will be there for three orf four days, and will probably be staying in a hotel somewhere near downtown for free, so lodging tips are the one thing I am not looking for. We decided on DC because it is in driving distance, we won't feel like the kids are missing out on it (they are too young to appreciate it), and we know there is a lot to do and see for free. We would love to take advantage of as much of the free stuff as we can, but will be willing to slurge here and there.
Thanks everyone! I will take any and all information you would like to share!