Agreed with Navin. Do not waste part of the day flying to another island.
Have only been to Kauai once so there will be others who know the area way better but stayed in Poipu at the Sheraton. It's for the tourists but there are very nice spots to eat nearby at The Shops at Kukui‘ula. a little farmer's market there as well that I'm sure they still do.
Def hit up the north end of the island by car (Princeville and Hanalei) very, very beautiful. Can easily fill a day up with that.
See the Napali coast from the water, there are tons of snorkel tours that take off from the towns on the south side of the island that wrap around the island. This is a must do IMO.
If you do end up going to Maui or Big Island I have all kinds of suggestions
Enjoy!!