I have spent part or all of every summer of my life on the outer Cape. I don't know much about the lower Cape, but if your travel brings you out to the tip, I heartily recommend:
amazing fried clams and decadent fried scallops at Arnolds in Eastham
delicious nouveau Italian seafood at Terra Luna in Truro
unbeatable lobster dinners at Moby Dicks in Wellfleet
ubiquitous and beloved rollwich sandwiches for lunch at the pond or beach, by Box Lunch (esp. Wellfleet locations)
lobster roll at Mac's Seafood on the Wellfleet Harbor
a tiny, innovative, menu changes daily place called Sol, also on the Wellfleet Harbor
tasty, ginormous burritos for people watching on the street or sunset watching over the bay at Big Daddy's in Provincetown
even if you don't have a place to cook (and grilling your own fresh fish is one of the best ways to eat on the cape), go take a look at the gorgeous fish and produce at Hatch's in Wellfleet - truly a wonderful market, and they will shuck a couple of oysters for you to slurp right there for like a buck a piece.
If you have some more parameters of cuisines etc, I can aim to be more tailored to what you're looking for. Have fun!