We went last year for my parents' anniversary. We island-hopped, so were only on Kauai for 3 days. Here's an email I sent to a friend recently. It's truly one of the most beautiful places I've ever visited.
Sounds like like you are already doing Na Pali coast via helicopter, which I would definitely recommend.
And you must do Waimea Canyon. It's only accessible from one side of the island, but it's the side you're staying in. IMPORTANT: The best views of the Canyon will be before noon; clouds often roll in in the afternoon. There are several lookouts along the road, we stopped at most of them. The "ultimate" view is at the Kalalau Lookout; the Waimea Canyon Lookout is the most panoramic. Make sure to take a jacket—it can get cool at the higher elevations!
We also did a whale watching tour from Port Allen, but I’m not sure when whale season season ends. It felt great out on the water and the deep blue color was spectacular.
We stayed in Princeville, and third Hanalei. It's a cute town w/some restaurants/cafes. Haena Beach Park is a great spot to watch surfers; Cannons, one of the most famous surf beaches in the world, is just past Haena Beach. The surf report is handy to follow to see the best surf times. http://www.surfline.com/surf-forecasts/kauai/kauai-north_3203 You’ll have to go pretty early to catch the surfers. But when you’re done, you can stop into Hanalei Coffee Roasters for great coffee and pastries! (Hanalei is about 1 hr 15 min drive from your hotel.)
We’re not hikers, but I'm sure that info is easy enough to find. Use the Local Experts service (they are contracted to most hotels as the concierge service) is incredibly helpful. The service is free; we just tipped. The Local Expert at our Hilton in Waikiki booked all of our activities on every island. Very knowledgeable, friendly and professional.
Food:
This is a list places we actually went to. Below that is a list of recommended spots/foods from friends.
• Hamura Saimin - in Lihue; Hawaiian ramen. You can see menu/pics on the TripAdvisor listing. Save room for the lilikoi (passionfruit) chiffon pie.
• Kauai Beer Company - in Lihue; fun local beer tasting, close to Hamura ramen place
• Ishihara Market - in Waimea; this is an actual market/grocery store with a wide selection of prepared fish/poke/prepared items in cases in the back (I recommend getting a cheap styro cooler to keep in your car so you can take fish/poke with you) I would totally eat this food every day.
• Tiki Tacos - in Kapa'a; delicious tacos, handmade tortillas
• Pizzetta - in Koloa, very good pizza; we got it to go to take back to our condo after a long day visiting Waimea Canyon
• Shrimp Station - in Kapa'a (just around the corner from Tiki Tacos); for local favorite dish garlic shrimp, pretty similar to shrimp scampi.
Where to eat
• Lots of seafood, roast pork, fruity/spicy sauces; lots of interesting fruit; macadamia nuts
• Beach House (Poipu) - http://www.the-beach-house.com/
• Da Crack (fish tacos)
• Neide’s Salsa and Samba Restaurant (Hanalei) – http://www.resource4hawaii.com/websites/neides/ Brazilian and Mexican; nothing fancy, great view
• Oasis on the Beach (Kapaa) - http://www.oasiskauai.com/
• The Dolphin (Hanalei) - http://www.hanaleidolphin.com/index.htm
• Bar Acuda - http://www.restaurantbaracuda.com/
What you want to eat in Hawaii (specialties/local faves) (http://www.seriouseats.com/2014/12/hawaiian-cuisine-local-food-what-is-spam-musubi-poke-huli-huli-saimin.html):
sushi
fish tacos (w/ono, mahi mahi, or tuna)
poke
mochi
fresh tropical fruit
macadamia nuts
poi
manapua (pork buns)
musubi (spam onigiri)
saimin (Hawaiian ramen)
huli huli chicken
garlic shrimp
loco moco (rice/meat/gravy/eggs)
malasadas (donuts)
shaved ice