Hey Taylor,
You need to do a bunch more research before you do anything else. I used to live in the area (at one time, the four house down from Mystic Seaport). You can easily blow a day at the Seaport. There is no way you can even nearly do Mystic and Newport in the same day. it may only be 50+ plus miles between the two, but it is not all E-way. Going back and forth as your plan shows is a big waste of time.
You are also missing the submarine museum in New London and WHOI. You need to re-evaluate your effort level.
Matt (BTDT)