Where should we stay on Kauai?

Stay in a location where you'll not be disturbed.

Everyone has well meaning family members, but remember, not only are they attending your wedding, they’re also on a "VACATION". So if you’ve booked a vacation home for the family or a suite of rooms at a hotel, just consider that from the night of the wedding on, find a separate place where you can have some privacy.

It might be a good idea to each blame the other when you're asked where you're staying, - "I just don't know, he’s booked somewhere as a surprise" - "I've left it all up to her guys, I don’t know where we’re staying for the Honeymoon, it’s a surprise" - that way at least you won’t have to worry about the tap on the door at 7:00 AM with a shout of "Hey you two, let’s go for that hike we talked about!".

Past that you could find a little hideaway like the Kauai Country Inn to stay at, or search through vrbo.com for a small cottage somewhere in the mountains that has no phone...

If you must stay at a hotel, you can’t do much better than the Grand Hyatt in Poipu, with 52 acres of grounds with lakes and great restaurants.
Whatever you choose, have fun!