I'm not too sure about hotels, since I grew up in Washington and whenever I visit I either stay with family or friends, or my company pays for hotel if it's for work. But I know there are a lot of hotels just across the river in Crystal City, which is just a couple of Metro stops from downtown. You might be able to find deals on some of the travel websites.
As far as what to see: Any of the Smithsonian museums are worth seeing. Personally, I like the American History Museum and also the art museums. The good thing about the museums is that they're all free, and you don't need tickets. So you can go for half an hour to a museum - you don't have to feel like you need to spend hours there because you paid $15 to get in.
Any of the monuments and memorials are worthwhile too. The Lincoln and Jefferson Monuments, and the FDR and Vietnam War Memorials are all especially worthwhile. Again, all free and no tickets are needed. All of the museums and monuments are located within a block or so of the mall.
And of course, the U.S. Capitol, White House, or Washington Monument are all right near the mall as well. You DO need tickets for these three things (they're all free, but you need tickets). For the Washington Monument, you can only get tickets the day you want to see it - you get them from a kiosk near the monument. This, to be honest, is overrated - it's nice and all, but considering the amount of time you will probably have to wait in line for tickets and then waiting to go up (probably will take all day), it's not worth it. You can still of course see it from the outside, tickets are only needed to go inside. The White House and Capitol tickets are also free and it's "strongly encouraged" that you get them in advance, and considering the fact that it's peak tourist season in Washington, I'd say that's a good idea. You can reserve them online - just google "White House tours" or "Capital tours". The Capitol has a new visitors' center which you can see without a ticket - but for guided tours of the chambers and other cool stuff you do need a ticket. Again, all are free though.
So anyway - there's plenty to see in Washington. You could easily spend a week there and not see everything but at least you have a start! That's the best time of year to visit Washington in terms of weather and seeing the cherry blossoms. Of course, as I mentioned, that also means it's peak tourist season - plus it's spring break for a lot of schools, and Easter weekend as well as Passover, so it will probably be quite crowded. So if you're planning on driving (which is never easy to do in the Washington area), it will be worth it to park at your hotel or at the Metro and taking public transit. Fortunately the Metro is easy to use, convenient, and all of the tourist stuff is walkable.