Some recommendations:
Duke's restaurant in Waikiki. I like their breakfast buffet. Good beach view if not too far from the railing. Opens at 7:00 AM.
Climb Diamond Head. They've improved some things since I last did it. No more super dark tunnel to walk through since they added lights. But it can be a sweaty hike, even in winter. The more direct sun is the problem, not the temperature. I suggest taking a small towel or at least a washcloth to wipe off the sweat.
The Pacific Beach hotel has a nice (and more expensive) breakfast buffet too. And I think they open at 6:00 or 6:30. There is a huge multi-floor aquarium in the restaurant which is kinda cool.
The International Marketplace (right across from Outrigger Waikiki) is presently closed for major renovating, but a little street next to it (Duke's Lane) has a lot of souvenirs. Might be considered a tourist trap, but some interesting things. Here's the deal though, never just pay whatever the price shows. I'm not much for haggling, so when asked if I want what I'm looking at or asking about, I always say, "I'll think about it while looking around some more". Many of the booths sell the same stuff so almost always they'll quickly drop the price and usually by quite a bit. I think the last time I bought something there, it was $25. As soon as I said I would think about it, they dropped the price almost in half!
You might want to go to the Aloha Swap Meet (at Aloha Stadium, close to where you'll go to the Arizona). Open usually Saturday, Sunday, Wednesday. Lots of the same stuff too, but you can buy perfectly good aloha shirts real cheap and t-shirts can be had for a few dollars - at least when I was last there years ago. Often 5 for $20 but I'd occasionally see something like 6 or 8 for $20.
For a luau, I like Paradise Cove out at Ko Olina area. But they've been doing a lot of construction on the highway in some area on the way and traffic can really get backed up, even fairly late. I don't think it is a problem coming back, but not sure.
Another luau option I like is up the windward coast at the Polynesian Cultural Center. I recommend that place anyway. Opens at 12:30 - at least that's when it used to open. You go around to the various "islands" for their shows and exhibits most of the afternoon. Definitely catch Samoa and Tonga! Very entertaining and funny. They usually have a "main" show at each and some have secondary shows. For example, I always catch the first Samoa show and then they'll typically follow it with a show about cooking (very interesting) or move you to a BIG hut where they go through cultural things, and I've also seen them do one on making rope and such. Don't miss the main show though.
Around 5:00, I think, you go to a luau (there is more than one there) that you paid for when you got your ticket. I've found most luaus are pretty much the same here, especially the food. But at the Polynesian cultural center, their luau is a bit different on the entertainment. Paradise Cove and others will have about 4 male and 4 female dancers. They do dances from Hawaii, Tahiti, etc. At the cultural center, it is only about Hawaii - and they have children (keiki) dancing too. It, frankly, feels more like family. But don't worry about missing the other stuff because all tickets include their "Horizons" night show. MUCH better than the other luaus I've seen, for two reasons. One is that it is stadium seating so the view isn't blocked much as so many luaus are. I've sat in the very last row - which is far back and high - as well as maybe 8 rows back and both were very entertaining. The other benefit is that it is BIG. They have a couple hundred dancers and some pretty large groups on stage at the same time. This makes it far more effective, in my opinion. They cover dancing from 6 islands as I recall (Hawaii, Samoa, New Zealand, Tonga, Tahiti - and I forget the other one! Maybe Fiji).
One thing about Polynesian Cultural Center - you can have the problem of hours in some pretty direct sun and not a lot of places to sit in shade. If you can get a shady spot at an outside show, grab it! By the time you get to 5:00 you can feel worn out enough that you don't want to stay. You may have less trouble with this at your age, but doesn't hurt to use caution. Once the sun drops behind the trees, everything is fine again. Definitely stay for the night show though.
Near Waikiki is Tantalus. There is a big looping road that goes up about 5 miles from where I measure it. On the left side (as you face Tantalus) is Tantalus Drive. On the right side is Round Top Drive. The name changes at the top. If you go up the Round Top side, about 2.6 miles or so is a park (you'll turn left to enter it). There is an great view here. Actually, there are two parking areas. The first is where the rest rooms are and you can walk from there easily to the lookout. Or park at the lookout itself. For comparison, Diamond Head is about 750 feet high. The lookout is over 1100 and you have a big panoramic view. The grassy area in front of the lookout platform is also the location of a picnic scene with Elvis Presley from "Blue Hawaii".
Hanauma Bay is good for snorkling, but if driving be aware that when the parking gets full, they close it until some others drive out. You can get there by bus from Waikiki. It is about 11-12 miles from the middle of Waikiki. If you take a bus, it could be crowded coming back - to the point where you have to wait for the next bus. So here's a trick. Catch the bus that is coming from Waikiki - that bus will continue on to Sea Life Park which isn't far away (and some nice views if you sit on the right side). Then it turns around and comes back into Hanauma Bay, pretty empty since everyone has gotten off there before or at Sea Life Park. So you already have a seat and don't have to worry about waiting for another bus.
Shave ice - Matsumoto's on the North Shore in Haleiwa is probably the best known. Of course, every has their preferences but I think more people go there than anywhere else - usually quite a line! I like it a lot. Get it with ice cream and condensed milk! You can get azuki beans, but I didn't care for them. My other favorite is Uncle Clay's House of Pure Aloha. They make their own syrup from berries and it is really good. They are actually on the way to Hanauma Bay in the Aina Haina Shopping center. Just off the main road (Kalanianaole Hwy).
I think Haleiwa is a neat town to visit, whether getting shave ice or not. They also have a Mexican place I like (Luibueno's).
Oh, and if you just want to get a pizza, I recommend "Big Kahuna's" on Paiea St (right by the airport). No connection to me - I just eat there a lot! They make really nice big sandwiches too.