A few random thoughts:
I have taken the Cross Sound Ferry many, many times. It does not save you a lot of time overall, but it is MUCH more relaxing than driving. I highly recommend it.
When you arrive in New London, there is a very good lobster and seafood restaurant not far from the ferry called Captain Scott's Lobster Dock. It's worth a stop for lunch. Note that it's super casual (a "clam shack" as we call it in New England), and all of the seating is out doors.
http://www.captscotts.com/Pages/Default.aspx
Not far from New London is Mystic, Connecticut. I've never been, notwithstanding having lived in the Northeast United States for most of my life, but it's a major tourist attraction.
If you drive up the coast through Rhode Island, rather than the more direct inland route to Boston, you can detour to Newport, Rhode Island, which is worth a stop for an evening. (On a recent visit, I stayed at the Cliffside Inn and enjoyed it very much.
https://www.cliffsideinn.com/)
Provincetown might be nice for a night, but it still will be off season when you're there (which could be a good thing, depending on your perspective), and you have to consider how much driving you want to do; it's not a short detour.
Boston hotels are very expensive that time of year principally because Boston has so many universities that have graduation ceremonies in May.
To save money in the Boston area, you could stay in the suburbs and take "the T" (public transportation) into the city. I use Hotwire.com with great success in the Boston area. Hotwire offers unsold hotel rooms at discounted prices, but the catch is that they don't tell you which hotel you're getting until you've already committed to and paid for it. Here's what I recommend to eliminate any risk:
(1) search in Boston for the dates you want (you're usually better off waiting until the day before arrival to get the best rates);
(2) once the results appear, click on "Filter by Guest Rating" and select "9 out of 10" (I find that as long as I select a hotel with at least a 90% approval rating, I'll be completely fine;
(3) click on the shaded area of the map that is labeled "Waltham - Newton - Wellesley." These are suburbs directly to the west of Boston and provide for excellent access to Boston, whether by driving or by public transportation.
Almost all of these hotels will offer free parking, and many will include breakfast. Based on my own experience, if you are offered a "3.5 Star Boutique Hotel" with those search parameters, it will end up being the
Hotel Indigo Boston Newton Riverside, which is directly next to the Riverside Station on the Green Line of the T, making getting into and out of Boston very easy. (You could of course book directly with the Hotel Indigo, which might be more expensive but would eliminate the risk of being assigned a different hotel on Hotwire. But even if you're assigned a different hotel in the area, you easily can drive to Riverside Station, where you can park at a reasonable cost, and take the T into Boston.)