When we lived in Lihue we would typically take our visitors on a tour up to Waimea canyon, and Kalalau lookout. From Lihue we’d head west on Kaumualii highway and make a stop just past Kalaheo at Kauai coffee. It’s a great spot to sample Kauai grown coffee, and hit the bathroom. Next, we’d go to Waimea and head up 550 and drive all the way to the end without stopping until the Kalalau valley overlook (Puu O Kila lookout). We found it’s usually less cloudy earlier in the day, thus the beeline to the top. We’d then head back down the canyon and stop at the various lookouts. On the way down we’d go right on Kokee Rd which goes to Kekaha. Once back at Kaumualii Hwy go right to check out Kekaha beach. Turn around whenever you want, then head back east towards Lihue. We personally rarely stopped in Hanapepe, but you could if you want, On the way back, time permitting, you could drive down 520 (the tree tunnel) to Koloa, and possibly Spouting Horn. Once back to Kaumualii Hwy go right, and then right on Kipu Rd, then a left on Hulemaulu Rd. Follow that all the way back to the port while stopping to see Menehune fish pond.
A nice alternative is a south side beach day and hike. Poipu beach has life guards, good snorkeling, and more often than not monk seals. A really nice hike along a rocky coastline is near the Hyatt at Shipwreck beach in Poipu. Just follow any trail near the cliff and go as far as you like. We avoided the beach there especially in the summer due to the rough water.