I love a good botanical garden, and the munchkins love them too. We've made a point of seeking them out on every trip, from Seattle & Vancouver, up & down the Eastern seaboard, to New Orleans to Italy, especially enjoying the children's activities like the flora & fauna scavenger hunt in North Carolina pictured here:
We also enjoy a good arboretum, like the U.S. National Arboretum in Washington DC that we visited in 2012!
Not sure where the nearest public gardens are to you? Better Homes & Gardens has this very useful Public Garden Locator with links to the gardens so you'll know hours, what's blooming now, etc.!
I didn't realize that we have 3 universities in CT with gardens or an arboretum - we'll pick one of those for the 10th and head over there right after school. Have a quick peek at the list - you might just discover a new favorite public garden to visit!