We visited Kauai a couple of years ago and rented a car and it was the best idea ever. We were there overnight so that helped alot. the only problem we encountered was the delay for the rental car company to pick us up once we docked. We waited about an hour, but after that Kauai was ours to explore. You need to research all you want to see and plan your trip from there. We spent the first day exlporing the eastern side of the island with the many waterfalls, lighthouses, coastal views, fern grotto, etc. Most of the shops close by 6 so for us there wasn't much nighttime driving. The next morning we went west and went to the canyon, which compares to the Grand Canyon.
Renting a car on your own is the best deal compared to excursions from the ship and you are in charged. Kauai is not called the Garden Island for nothing, enjoy your trip