If you are in port at Nawiliwili for the day, you have time for exactly one good region, not the whole island. Ships dock right at the pier (no tender), and most are in port roughly sunrise to sunset, so plan an out-and-back you can finish with hours to spare. Here are three honest options depending on whether you want to walk, swim, or see the famous scenery.
Nawiliwili Harbor is on the southeast coast. Downtown Lihue is about a 10-minute drive (roughly 2 miles), and the nearest beach, Kalapaki, is a flat walk of about 10 minutes from the pier. Poʻipu on the south shore is about a 30-minute drive. The north shore (Hanalei) is closer to 45 minutes to an hour each way, which is doable but eats your day. Since the island has no cross-island road, do not try to 'loop' it. Pick one direction.
Kalapaki Beach is an easy, flat walk from the ship, in front of the Marriott. A breakwater shelters the bay, so the water is usually calmer than open coast, which makes it a comfortable swim or beginner snorkel and an easy place to be back aboard quickly. It is the safest bet if you do not want to rent a car or book a tour. Still check the day's conditions, because calm is never guaranteed.
If you want the best water, Poʻipu is about 30 minutes away and tends to be sunny with good snorkeling, including a decent chance of seeing turtles. Lawaʻi Beach is another south-shore snorkel spot nearby. This is the strongest in-water day-trip from the port, but always check that day's surf and posted signs first, since south-shore swell and shorebreak can make it unsafe. Leave a generous cushion to get back to the ship, since you cannot miss the all-aboard time.
For the classic Kauaʻi views without much swimming, Waimea Canyon is about an hour west of the port, or book a short helicopter or boat tour that returns you to the harbor area. Tours are the only way to see the interior and Na Pali, since most of the island is roadless. Book a port-friendly operator that guarantees you back before all-aboard, and choose a morning departure for clearer skies.
Build in a big time buffer; the ship will not wait. Carry water, mineral reef-safe sunscreen (Hawaiʻi bans oxybenzone and octinoxate), and a little cash. If you see a Hawaiian monk seal or sea turtle on the sand, give it room; federal guidelines say stay 50 feet from monk seals and 10 feet from sea turtles. And if the surf is up, the calm harbor beach is a better idea than a far-off coast you have never seen.