Loved my time in Kauai, though we didn't do much besides hang out at the resort(Marriott's Waiohai Beach Club).... Poipu Beach is really nice. We did go to Waimea Canyon, Kalalau Lookout & Tunnels Beach...but most our time was spent at the resort with a beer and I smoked a fair number of cigars watching the time pass. You said you were not planning on golfing, but I thought I would mention that we did, Kauai Lagoons Golf Club, which was great. Though since I always golf at 4200' give or take, golfing at sea level is humbling.
Dinners at the Beach House
http://www.the-beach-house.com/ & Tidepools (restaurant in the Grand Hyatt Kauai) were memorable. I would recommend at least a dinner at each if you can, get reservations at sunset.
As
MikeyC mentioned above,
Brenneckes is a cool place. We spent quite a bit of time there, it was just a short walk from where we were staying and I enjoyed their atmosphere.
As far as the Kauai Cigar Co., your results may vary....
Though I have seen positive reviews, I wouldn't pay $1 to smoke another.
http://www.cigarasylum.com/vb/showthread.php?t=35844
I thought cigar pricing in general was VERY expensive on the Island, as was about everything.
It is a wonderful place, ENJOY!