Nice and clean, Xanadu, check. Palm trees, Xanadu, check - also some jungle-type foliage, very cool. Bar/restaurant, Xanadu - NO, but very near and your patio decks and the pool area are very condusive to making your own fun. Also Xanadu is a nice walk to town, very close to a little grocery store, and kinda situated in between center of town, and quite south of town, which gives you lovely options for walk-about, cart-about and such.
Xanadu's beach is not the same as some other places, inasmuch as it has a bit of a seawall, but the sand is kept beautifully, and there's a lovely dock for sunbathing and swimming.
I have no affiliation with Xanadu, other than I admire the place and it would seem to meet most if not all of the requirements of your group . . .and possibly some things you hadn't even considered.