Not warm, but NYC and DC are great for kids
Williamsburg is nice. The weather could be up and down, but usually averages about 70. Busch Gardens will be open, and Colonial Williamsburg and Jamestown should interest a ten year old.
This is Williamsburg's huge anniversary year so historic Jamestown and Yorktown are particularly nice this year. If you decide to go, PM me and I'll offer some more suggestions on other things to do. My youngest just turned 12 so I can tell you what we like. FYI - The schools in Williamsburg are off the first week of April (just in case you want to be with or without the local student crowd.)
Another suggestion -- two years ago we did NYC over Easter break and loved it!! Not warm or swimming weather, but depending, it could be quite pleasant. There are several Marriott hotels right in the middle of the city. Our visit included Statue of Liberty, Ground Zero, NJ science museum (forget the name, but it is right across the water from Statue of Liberty and was phenomenal on Easter Sunday), Central Park, fun chocolate drink place (forget name), Sony lab, NYC diners (so fun!), etc. Wonderful trip. I don't recall - boy or girl? NYC also has the American Doll store, a huge ToysRUs, ESPN Zone, etc.
Another not so warm destination but great - Washington DC. All the Smithsonians are free and could fill several days if you enjoy museums. There are usually special activities for kids, too. We typically do that in early October, but if you get lucky you may be able to enjoy the Cherry blossoms! There are other interesting places to visit as well.
With kids just older than yours, let me know where you choose because if I've been there I'll have already researched it and picked out the best stuff to do!