Public Transportation has improved much on Kauai in the last few years. The Kauai Bus operates bus routes covering the island from Kekaha to Hanalei, Mon. thru Sat.. Service begins around 6AM and ends around 8PM-10pm depending on your pick up area. Sunday and holiday service is not as frequent but available. Buses are on time and the ride is enjoyable, they even have a Hybrid bus. 

Buses will not allow luggage on board, but many taxis are waiting at the airport to get you to your hotel when you arrive.

http://www.kauai.gov/Bus