There are a lot of places around New England where you can get beach and good weather. These cute little cottages in Truro right on the bay beach are just right for two
http://www.capecodrental.com/SearchR...asp?Town=TRURO
or you can go to Maine. It is a lot easier and may be cheaper than the Cape.
Just getting on a plane may be nice, but know that if you get a low price to Florida for airfare, and then factor in a very low price hotel, you will still need a rental car and here is the ugly part: Florida is very hot and humid in the summer. You may not want to be outside too much.
Also agree that June will be less exspensive than July. Since most colleges get out in April, try for June to save money while the grammar school kids are still in school (which they might be until July 4 this year because of all the snow.)