Had some time to kill myself there back in September. I opted for one last swim before I headed to the airport (it was incredibly refreshing). The beach was a public beach called "Kalapaki" and is located right in front of a Marriott. You can easily park in the adjacent Anchor Cove Shopping Center (I bought a super cheap towel there to dry off, and then disposed of it of since I didn't want to stuff a wet towl back in my checked luggage). If swimming before the flight isn't your thing, I also went for a nice jog on Ninini Point St. which runs alongside the airport perimeter (and the Marriott golf course), so you get to see some pretty cool airplane action. The path is also great for walking. For a place to park, lookup Kauai Lagoons Marina on your preferred map app.