That's Great Island out there, across from Chequessett Neck. I have done the Great Island long walk several times (8-10 miles). Last time, we saw the resident Great Horned Owl. On this trip, the heat defeated us before we got very far.
I recommend the hike as a way to immerse onself in the salty, piney goodness of the Outer Cape. (Bring hat, sneakers, and backpack with water and things to munch, or you will regret it.)
For me, my annual trek to the Cape is an annual (pagan?) re-baptism. I lived there until I was 5 or 6 (do not remember a thing), but have returned almost every year since then, often with extended family and often not. I believe I converted the now-Mrs. BD to me partly by taking her up there.
Or maybe it was a test to see whether the lovely, spirited young Jersey gal could love something that I loved. She did. Still does.