I think that Cape Cod may be of interest. It's truly a special place. And the nice thing is that there are so many "what to do on Cape Cod" online articles.
Here's one of many:
An insider's guide on the best things to do on Cape Cod, including best boat tours, whale watches, beaches, food, attractions and tons more.
newenglandwanderlust.com
Whale watch and other boat rides, incredible seafood and other restaurants, bike riding trails, the country's best prospects playing summer Cape League baseball, great beaches, fascinating hikes (including dunes hikes where you might just as well be in outer space), multiple ice skating rinks open during the summer, cranberry bog tours, cooling sea breezes, etc., etc., etc.
As you may know, Cape Cod is shaped like a Captain Hook hook. South and east of the hook is the direct Atlantic oceanfront. Strong waves, somewhat warmer water than north and west of the hook.
The bayside has relatively little wave action making it perhaps more suitable for younger kids.
If you stay closer to Plymouth, then you're within shorter driving distance to Newport or Boston for a side trip (to see the Red Sox play the Yankees or Mets, for example). But if you'll be pretty much staying on the Cape, being centrally located may allow you to explore the whole Cape, including Provincetown at the very end of the peninsula. As to the latter, you won't often see it mentioned, but some visitors can sometimes be flamboyantly gay, which gives PTown a fun and quirky vibe, but I'm not sure it's the best place for kids. Kids visit there with their families, and even live there as it's the headquarters for multigenerational Portuguese fishermen, but things can be seen that aren't seen elsewhere.
Many New York and New Jersey residents come up to the Cape. There used to be MANY French Canadians coming down to the Cape from Quebec. Which made it doubly fun for kids as they tried to communicate with exagerrated facial expressions and hand signals. Don't know if the French Canadians are still coming down as I didn't visit the Cape last summer.
I would check out the reviews for timeshare resorts but having a direct oceanfront view would be ideal.