First, a question for you: you're there now? Because if you're talking about the Kalalau Trail when you reference the trail to the NaPali coast, it's currently closed and may be into early 2019.

My wife and I had a great experience with Jack Harter Helicopters, for what it's worth. Regardless of the company you go with, do doors off. Also driving between Poipu and to Hanalei for the NaPali in one day is doable, but it seems like you'd be rushing, yeah.

Also, if you haven't picked up the Kauai Revealed guidebook, I can't recommend it enough.

Get this book: The Ultimate Kauai Guidebook: Kauai Revealed

It is SUPER helpful. That being said our highlights from our trip were the helicopter ride, ATVing, and kayaking. I highly recommend kayaking the Wailua River to Secret Waterfall, we just rented the kayak and did it ourselves rather than do an official tour, super easy and nice to go at our own pace, prepare to get muddy lol. I also highly recommend spending at least a day to drive up Waimea Canyon and hike around, the views are jaw dropping (see my post history for my engagement pictures there). There’s also a great restaurant nearby that’s a little hole in the wall place called Da Booze Shop, great place to refuel in between hikes.

Edit: I forgot to mention if you’re a dog person and have some flexibility in your schedule you can check out a dog at the Kauai Humane Society and take them on a field trip. We did this and took him to the beach, it was a blast.

I concur with the others. Save the other island for another trip. Maui is probably better for most honeymooners, but unless you really hate nature you're going to love Kauai for the 6 full days. Get the The Ultimate Kauai Guidebook: Kauai Revealed and choose your activities. I recommend the Smith's Kauai Luau.

I went there for 2 weeks in June. Spent about $800 total, housing included. But the number will vastly depend on your needs. Will be renting a car? Rental rates are very cheap on the island as there is fierce competition. I paid around $250 for a week even as a younger driver. Hitchhiking is also very prominent, and there is a very affordable shuttle bus along the main highway during certain hours (ends around 9pm). Food is plentiful and honestly not insanely expensive if you are able to find the places locals eat. Highly recommend [this] (https://www.amazon.com/Ultimate-Kauai-Guidebook-Revealed/dp/0996131841?keywords=kauai+revealed&qid=1536774895&sr=8-1&ref=mp_s_a_1_1book) for an extremely thorough look at pricing specifics. Enjoy your trip though! I'm having a nasty craving for chicken in a barrel at the moment.

So many! I found our itinerary from 3 years that I'll copy from. We were incredibly lucky in that there wasn't rain for 3 weeks prior to us getting there so none of the trails were muddy but make sure you bring shoes you don't mind walking ankle deep (literally) in mud. We referenced this book to come up with our itinerary because our friends suggested it to us and I highly recommend it.

Hotel

Hilton Garden Inn Kauai Wailua Bay

This is where we stayed and we were super happy with it. It's right next to a beach park and we got to watch the sunrise every morning on the beach listening to the waves. The hotel provided us with a straw beach blanket and a cooler and we used that throughout our trip. Also it's walking distance away from a strip mall that had a lot of good food options. We were able to walk there every evening for dinner which was nice since we didn't have to drive.

Food

Lava Lava Beach Club

The happy hour is amazing. The prices are super reasonable (don't go for dinner or lunch, the prices are absurd). You get to have the toes in the sand experience with $3 mai tai's and super yummy appetizers. I can't explain how much we loved this place. We still talk about it to this day.

Hikes

Pihea Trail

This was by far our favorite. It's basically bouldering throughout the entire hike which was awesome. Be prepared to get muddy!

Kalalau Trail

Unfortunately we didn't get to do this since it was closed for trail maintenance but apparently it's a must. We want to go back just to do this trail. Word of advice, check online to make sure it's open before driving all the way out there.

Group Activities

We booked two group activities because we didn't want to rent our own kayaks or stand up paddle boards and we wouldn't have known where to go with them. We had a blast and the guides we had were fun and I highly recommend it:

• Kauai Stand-Up Paddle Board Tours – Downwind River Adventure
  
• Wailua Waterfall Kayak
  
  There's a ton more to do and if you are interested I can share my itinerary with you, I didn't want to make this post too long (too late). There's a lot of great ideas in the guide book. Let me know if you have any questions!