First Congrate. Have a great time. Do not know what you like to do. Down south you have Waimea Canyon. To do this properly is about a day. Take a picnic lunch. Drive to the top. Resist the turn outs. Drive as far as you can and then hike past the top parking a bit. There are several View Points up there. Have your picnic lunch in the Park at the top. Then stop at all or most of the View Points on your way down. There is the Kauai Coffee Planation. I do not know how old your child is in the picture. There is zip lining in Koloa. There is an inner tube float down the old sugar cane canals in Lihue. There is Poipu Beach. There is the Alakai Swamp Trail. There are Cruises out of Hanalei Bay to the Napali Cliffs and snorkeling. There is the Spouting Horn. There is the Mala'ulepu Trail that starts on the top of the Cliffs just north of Shipwreck's Beach. There is the Makauwahi Cave. So this is a week's worth of stuff for 3 days.
Luau: some of the large Hotels have Luau. The two I would recommend are Kilohana just outside of Lihue or Smith Family by Kapa'a. Kilohana has the more traditional entertainment telling the Polynesian story through song and dance. Smith Family has greater diversity to honor the many people that have emigrated to the Islands. Rem3mber Poi is not a dish by itself but to dip your Pork.
Up north. There is Anini Beach. The town of Hanalei. The beach at Hanalei. The Road to Ke'e Beach (end of road) may or may not be open. There were major storms last April that caused a lot of damage on the north shore. Kayaking up the Wailua River to the Fern Grotto and Secret Falls. It is about a mile hike to the falls. Sometimes the trail is very muddy.
In Lihue there is a Costco. Cheapest gas on the Island by a lot.