The best meal we ate at Cape Cod in Massachusetts was lunch in Eastham at a place called BoxLunch. I had read about the franchise before we went and had to check it out. Apparently their specialty, the "rollwich" (a rolled sandwich), has its own history in the area as a convenient packed lunch for fishermen. Darren had the Lobster My Way Rollwich for $11.99. Very fresh and very tasty cold lobster with lettuce, tomato and mayo inside a thin pita roll.
If you're not such a big fan of lobster or just want something different that's cheaper, they've got plenty of other options - most around the $5-$7 mark. I got the Turkey Club Rollwich for $6.79 which had turkey, bacon, American cheese, lettuce and tomato. Yum!
If you're in Cape Cod and want something healthy, tasty and reasonably priced, check out BoxLunch. We went to the Eastham location but they've got several locations on the cape. Well worth a try and perfect for a beach picnic.