Kauai is a great island to explore on your own, there's a really chill vibe and plenty of outdoor activities to keep you busy. I'd recommend checking out the Kalalau Trail along the Na Pali Coast, it's a bit of a hike but the views are totally worth it. If you're not up for a long hike, you can also take a boat tour or kayak along the coast, which is a great way to see the island from a different perspective. Kauai also has some amazing beaches, like Hanalei Bay, where you can relax and soak up the sun, and the town of Hanalei has some cute shops and restaurants to explore, so you can easily spend a day or two just hanging out there.