Do not even think about riding there, during the summer, unless you go out before 5:30 AM. Trust me on this.
I spent every summer of my childhood/teen years at the Cape. Then, when I moved back here, every vacation with my kids. Now, I rarely go, except in the off season.
Stick to the beach on the weekends, have a barbecue, and if you do go out for dinner, go to a place where you can make a reservation.
I second the National Seashore. Also, the Audubon Sanctuary in Welfleet. Miles of flat, beautiful hiking, and if you time it right with the tides,you can walk pretty far. Last summer I hiked on the Pamet Area Trails in Truro. Go here, if you want a spectacular, harder/hilly hike to escape your family. It is rare for me to go to a place on the Cape I haven't been to before. Sandy, dune hiking, with a view to die for.
Go to a beach on the bay side at least once, when the tide is low. It is amazing. I like Crooks Brook Beach in Eastham.
Rt. 6A from Dennis to Brewster for antiques/art. There is a natural history museum on 6A in Brewster. The Brewster General Store.
Stay off of Rt 28 as much as you can.
Chatham Center/Main St. The Penny candy store near the rotary and the Fudge store. Seriously. You can have it shipped anywhere. Fun to people watch here.

Food: Bucca's for Italian food in Harwich. On Rt 28. No reservations. Go early/late, during the week. Sundae School. Yes, just what it says. There are a couple, but the one on Lower County Rd in Dennisport is the real deal experience. Don't eat before you go and order a blueberry Sundae, if it's in season.
Go to Bonnats' (spelling) in Harwichport for breakfast. Portuguese rolls.... do not miss this one!
Chequessett Chocolate in North Truro. The best hand made chocolate and coffee drinks I've ever had...
Arnold's for seafood in Eastham
Go to Provincetown. There is nothing else like it in the world.
If you are going to have one "fancier" family dinner, I suggest The Red Pheasant in Dennis. In an old house, with charm. It's been there for 40 years and never fails.
PM me for more.