Even though my visits are few and far between these days, as a Cape Cod native, I feel compelled to chime in. Chillingsworth is still pretty nice; my mom's best friend named it actually. I also like Ocean Edge, though I'm not sure I'd advocate staying in Brewster (kind of a no man's land between HYA and the cooler Atlantic spots). I suppose Falmouth is the only place I'd really advise against though, because it's so far removed from the rest of the Cape.
As far as must-sees are concerned, the whole coast guard beach area is worth exploring at some length, preferably by bicycle. Be sure to check out the Atlantic White Cedar Swamp.
And if you have a boat..... you might want to cruise over to Monomoy Island --> no people but some pretty cool old houses.
Oh, and Sandy Neck is also worth a visit even if the bay isn't as nice as the sound or ocean.