Yes, it is 100% necessary to rent a car during your trip to Kauai - that is, unless you plan to never leave your resort. Though Uber and public transportation do exist on Kauai, they are inconvenient! Uber is very expensive and there aren't many drivers out and about (especially very early or late). Public transportation is inexpensive, though the system does not specifically cater to tourists, so in order to get to where you want to go, you may have to walk a lot to and from bus stops; you'll also waste a lot of time waiting for the bus. While in Kauai, you should plan to rent a car. You'll have a lot more fun and freedom if you do! This is my favorite website for scoring deals on rental cars. Make sure to put Lihue Airport (LIH) as your pick-up/drop-off location!