For Connecticut, I am not a big fan of Mystic Aquarium. I think Boston Aquarium is much better - it has a big center tank that you walk around.
You might be interested in Gillete Castle state park (
https://www.ct.gov/deep/cwp/view.asp?a=2716&q=325204&deepNav_GID=1650 } very cool to check out the "castle" and the surrounding grounds.
Not far away is Goodspeed Opera House - sometimes tours during the day are available, depending on their show schedule. Speaking of which, seeing a show there is great.
As to "Plimoth" Plantation (Pilgrims) in Massachusetts, that is neat to check out but... they do the "living history" thing there, where the actors pretend to be pilgrims while you try your best to get straight answers about the houses, living, and history. I am not a big fan of that type of thing, I find it annoying. When you check out Plymouth Rock, make sure to ask one of the Rangers there about it. They have a very good 10ish minutes talk about the Rock.
The Pilgrims ship, Mayflower II, may not be there... I think it is still being rebuilt at Mystic Seaport in Connecticut... Speaking of which!!
Instead of going to the Mystic Aquarium, you could check out Mystic Seaport. The Mayflower II might still be there undergoing major repairs / rebuilding, otherwise there is almost always one or more interesting sailing ships there to check out, along with the small "village".