No, Strawbery Banke doesn't open until May 1st, unfortunately, it is a great place.
I'll third Odiorne State Park, and the drive along 1A anywhere from Hampton Beach north, including taking 1B through New Castle, stopping at The Great Island Common just for this view (and it is a lovely park too):
http://farm4.static.flickr.com/3215/...3ab0ee6a_o.jpg You can then continue on a mile or so north to visit Fort Constitution in New Castle:
Fort Constitution Historic Site - New Castle, NH. The fort notdancingqueen is talking about is Fort McClary:
http://www.fortmcclary.org/. The whole drive along 1A is really pretty, with some cool older mansions along the way - nice walking/biking trail along the ocean there too.
Also thirding Nubble Light House in York, and if you want some lovely nature walks, check out the Rachel Carson Wildlife Refuge, it has trails in Kittery and Wells, it's a really pretty area:
Rachel Carson National Wildlife Refuge - Visitor Opportunities