Congratulations on your upcoming wedding! DH and I spent a portion of our Hawaiian honeymoon at Aulani - trip report is in my signature.
Will we feel out of place as a couple w/o kids?
We certainly didn't. Much like WDW, all shapes, sizes, and family dynamics were there. You do have to be ok with having kids around and all that comes with it (i.e. noise), but if that's not a concern, you won't feel out of place at all.
How many days do you recommend (or, how many days is too many)?
We spent 6 days at Aulani, with 3 full resort days. This was perfect for us as we felt like we got to experience everything we wanted to at the resort, while still doing the most important sightseeing we wanted to do. We had also spent 3 nights in Waikiki at the start of our trip, so some of our sightseeing was done during that portion. I think if you just want to stay at Aulani without leaving, 3-4 days is plenty. Aulani is in Ko Olina which is an isolated part of the island, with very little in walking distance. You're essentially in a tourist bubble there.
What kind of excursions did you love?
I highly recommend a rental car which will allow you the freedom to do what you want. Aulani only offers a handful of organized excursions, so you lose any flexibility and are stuck with their times and offerings. They are also pricey, and some do not include transportation at all.
With that said, on our sightseeing days away from Aulani, we visited the North Shore/Dole Plantation/Waimea Valley on one day and Kualoa Ranch/Byodo In Temple/Kailua Beach on another day. We visited Pearl Harbor and Diamond Head through organized tours from our Waikiki hotel. Waikiki has many more offerings in terms of organized tours/excursions, and most of those offer transportation. We chose to do Pearl Harbor as an organized tour because they facilitated getting the tickets for us, and we chose Diamond Head as a tour because the bus drops you off at the start of the trail. Parking can be far and limited otherwise.
Aulani has two bars - Off the Hook and Olelo Room. We had drinks at both, but Olelo Room was more of the evening hang out with live music (Ben & Maila were amazing!). I will say that nightlife was non-existant at Aulani. Really, in all of Hawaii in general. There was nothing going on in Ko Olina after 8pm, and the resort was very quiet. We were usually back in the room by 9-10pm each night. It did allow us to have early mornings though, which was fine.
There is also Monkeypod across the street from Aulani which has two bars and a great happy hour! We ate there twice - loved the food!
We are not island hopping, but plan to stay at 2 different places on Oahu, or 2 different areas of the island. We are active and adventurous.
We loved staying in Waikiki because it has a very different vibe than any place else we visited in Hawaii. Two very different ends of the spectrum when compared to Aulani, so you'd get to experience both. Everything in Waikiki is walkable, and as I mentioned, tons of bus tours available to places that are not walkable. We opted not to have a rental car during this portion of our stay because of this, which saved us money because parking can be expensive and difficult in Waikiki. We stayed at the Waikiki Beach Marriott which we liked for its central location, making everything convenient. A lot of people love Hilton Hawaiian Village because of its resort-like amenities, but we knew we were getting that at Aulani so we decided against it. Plus, Hilton Hawaiian Village is at the far end of the Waikiki strip making for long walks. Next time, I'd stay the Moana Surfrider - beautiful, unique, and centrally located. The bar around the Banyan tree on the waterfront was awesome! If you decide not to stay in Waikiki, I still think its worth visiting at least once!
There is also Turtle Bay Resort in the North Shore which is beautiful. You may recognize it from movies. The North Shore was our favorite area we visited and would be good for hikes and other activities, but it would have a similar resort style feel as Aulani.
Since you're adventurous, that's another good reason to rent a car. Many excursions are designed for all types, so may be tamer than what you might want.
We're not big on character dining.
Same. We ate at the character breakfast at Makahiki and it was a mad house. Loud and chaotic. Reminded us of Chef Mickey's at WDW. We really enjoyed the non-character dinner buffet at Makahiki. Breakfast at AMA AMA was one of our favorite meals of the trip!