Given one way drop of charges for car rentals and the places you're looking to visit, you're probably best off getting and keeping the car for the entirety of your trip, with the possible exception of the Boston portion. Assuming you'll be flying from Boston, you could delay picking up the car if you do Boston first, or drop it off early if you do it last. The train isn't a particularly good option for logistical reasons, especially since you'll want/need a car in virtually every place you visit.
Without knowing exactly what your interests are, and going purely on the places you mentioned you wanted to visit, here is a *rough* itinerary to start from.
Day 1-3 Boston
Day 4-5 depart Boston, visit Rhode Island/eastern Connecticut.
Day 6 leisurely travel day toward Ithaca
Day 7-9 Finger Lakes, departing evening for Niagara Falls
Day 10-11 Niagara Falls, departing evening
Day 12-13 I'm thinking Adirondacks or Vermont
Day 14 depart Boston
Boston -->RI/CT - 2-3 hours
RI/CT--> Ithaca 5-6 hours
Ithaca-->NF 3 hours
NF-->Adirondacks/VT - 5 hours
Adirondacks-->Boston - 2-4 hours
You may want more time in Boston, and frankly I'm a little vague after Niagara Falls. These don't include specific destinations yet, that would require a little more feedback.
And I like how you distinguished between adults and twenty somethings :)