I was in Kauai a few years ago and rented a bike. I was with my 85 year old mother, so we got a single-speed tandem, but they did have road bikes as well. Sorry, I don't remember the name of the place, but it was near the public beach in Lihue. As others have noted, the main roads are busy. There's really only one road that goes about 3/4 of the way around the island; shorter spur roads lead up into more remote areas in the mountains. I seem to recall that there was an outfit that would drive you and your bike up to the end of Wiamea Canyon (about a mile above sea level; spectacular views), and you could ride your bike down the road back to the coast. Needless to say, that isn't what I rode with my mother! We stayed on a paved bike path that went along the coast out of Lihue, no cars and quite mellow, but only a few miles.