Nick -
Oversand permits for Cape Cod range from approx. $80 on Race Pt (limited availability) for the season to approx $160 on Nauset (public non-res). Dennis has a permit that runs $140-ish that provides access to Quivett and Chapin.
The Race is the best deal but for me it's almost double the drive and I stay mid-cape. I like fishing there but don't get up there all that often.
Dennis permit gets you to two great spots - Quivett Creek, just west of Brewster Flats and Chapin Beach, at the famous Bass Hole. You are allowed to be there at night as long as you are fishing and have a sticker. I've had the Dennis permit most years since moving back east to access the bayside beaches but this year I am going with Nauset.
Public access is at the Nauset Beach Parking lot, just down the street from our sponsor Nauset Angler. Non-residents can drive south to Chatham Inlet, quite the hotspot at times. It's the spit you see from the Chatham lighthouse to the left with the vehicles on it, across the inlet. Residents get to go north to Nauset Inlet.
Nauset is my family's favorite beach. I will get double the value out of the sticker by taking them to a great beach and might even get a blitz or two while we are tossing the frisbee, who knows ;-)