Regular taxi rates on Kauai are $ 3.00 per mile and .30 for every 45 seconds (.40 per minute). Poipu has limited taxi transportation. To get around Poipu when you want to go out to dinner either at Poipu Shopping Village (Roys, Keoki's Paradise or Tropical Burgers), The Shops At Kukuiula (Merrimans, Tortilla Republic, Dolphins, Josselin Tapas Bar & Grill or Bubbas Burgers), or any of the resorts and don't want to drink and driver, I recommend Pono Taxi 808-634-4744. They also do other various transportation to get to Koloa, or Port Allen for activity transportation (Capt Andy's, Holo Holo Charters, Kauai Sea Tours).
The only way to land on Kauai for most people is at Lihue Airport, which is located about 2 miles east of the town of Lihue.
Its airport designate is LIH, so when you are booking your flight, search for rates to get you to Lihue. Most likely, you will be connected via Hawaiian or Aloha Airlines, but there are also some direct flights on American and others.
By Air: United & American both have non-stop flights directly to Lihue, Kauai. Flights with Hawaiian, Alaska, ATA & Aloha require a connection in Honolulu.
By Car: A car is necessary to get around this island. Poipu Beach is 16 miles from the airport and generally under a 30 minute drive. Roads are one lane each direction so at times can back up especially if there is road construction.