Oahu Advice

ETA: as another tip: there is traffic on the highways and freeways. The peak traffic times are typically in the early morning, before 8:30am (when people are driving to work and school). And then again starting at about 5:00pm. (when people are getting off of work and driving home etc.)
So if you have to get anywhere by a certain time, at those times, plan ahead.
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http://www.gohawaii.com/oahu/experiences/culture
http://www.oregonlive.com/travel/index.ssf/2013/04/oahu_v...
http://www.royalhawaiiancenter.com/info/culturalprogramming
http://www.cnn.com/2012/06/05/travel/budget-oahu-activiti...
http://www.cbsnews.com/8301-500395_162-57508051/hawaiian-...

1) I would recommend going to see the "Iolani Palace."
It is right in downtown Honolulu.
http://www.iolanipalace.com/

2) And also seeing the "Bishop Museum."
http://www.bishopmuseum.org/

3) Also "walking tours in Honolulu":
http://gohawaii.about.com/od/oahusights/ss/honolulu_walk_...
http://www.aloha-hawaii.com/oahu/honolulu/
http://www.ohanatours.org/

Make sure you have a stroller for the 3 year old.

The Polynesian Cultural center is very visual and displays the various Polynesian cultures. Not only, the Hawaiian, culture. Hawaiians are not the same as say, the Tongans or Samoans etc. These are all different Polynesian cultures. Hawaii is a melting pot, of MANY cultures.
Per Hawaii, it is the Hawaiian culture, which is indigenous. And it was the Hawaiian Monarchy, which was overthrown by the outsiders. Thus, Iolani Palace, is the place to see and learn, about it.
The Polynesian Cultural Center, is quite a drive from Waikiki. It is on the opposite side of the island.... and yes it is an all-day into the evening type thing especially if you all stay for the Luau. And with a 3 year old in tow... it might be too long. Realistically.
From Waikiki, it would probably take 1 hour to drive there one-way. Also keep in mind traffic on the Highways.

4) Also just for fun and free is "Sunset On The Beach" in Waikiki:
http://www.sunsetonthebeach.net/

5) Also, the local Honolulu Police Department has free, tours- (and this is something not all Tourists know about):
http://www.honolulupd.org/community/index.php?page=museum
Also, while at the Honolulu Police Department, on the ground floor, there is a SMALL snack shop/store. THIS is where, you can find and buy "Hawaii Five-0" t-shirts and souvenirs. And also Honolulu Police Department souvenirs.
Finding Hawaii Five-0 t-shirts, is hard to find. Even for locals. There is no, Hawaii Five-0 stores.
So, this is a tip, for you. You can find it at the Honolulu Police Department's, snack shop/store.
And if you go here, bring cash. Because if I remember correctly, the snack shop/store only accepts cash. I went there with my kids before and bought stuff.

6) Hawaii is also full of very diverse foods. So, I would suggest TRYING all the different types of ethnic foods. Not only going to McDonald's to eat, for example. Hawaii is known for its good foods.
"Luaus" are a Hawaiian feast of traditional foods. Which is more commercialized now, for the mainstream palates.
It is not "Luau" food per say, that gives people food poisoning. Food poisoning can be derived from ANY food. Even an American style BBQ. It is about food preparation. Or the source of where the food ingredients came from. Or, some people may get "sick" from eating non-mainstream foods, because they are not used to it in everyday life.

7) I also recommend going to "Hanauma Bay" for snorkeling.
http://www1.honolulu.gov/parks/facility/hanaumabay/inform...
http://www.hanauma-bay-hawaii.com/
http://www.hawaiiweb.com/hanauma-bay-nature-preserve.html

7) Hawaii is not cheap. Yes it costs money. Even for locals. A gallon of milk, on sale is close to $6. Regular price it can be close to $8.
For example.
But in Waikiki, like all tourist spots, things do cost more.

You cannot, get a wide view or experience of the "Hawaiian" culture, with just one, venue.

Hawaii is very ethnic. Comprised of many many ethnicities and cultures. So be prepared to see many different "skin" colors. But yes, we all speak English. And don't go around in grass skirts.
It is also very casual here. Shorts and t-shirts and slippers is worn by most everyone. We do not dress formally here or wear suits and ties.
But be sure you all have comfortable covered shoes AND bring flip-flops (we call it slippers), because you will be doing a lot of walking.
And do not wear, socks with sandals or with flip flops.
This is "tourist" garb. And it will make you stand out.
And bring and use lots of sunscreen.
Even being out for 15 minutes in the sun, will get you sunburned.

If you have a rental car, also bring cash/quarters etc. Because that is what parking meters take. Or some meters take debit cards etc., but in Waikiki by the Zoo mostly.
There are also ATM machines everywhere.
Public restrooms are frequent. In any mall, hotel, or fast food chain restaurant etc.

8) Oh yeah, this is also a place to see/go:
The Mission House Museum
http://www.missionhouses.org/
It is about post-Hawaiian and the influence of the Missionaries in Hawaii and their impact on Hawaiians/Hawaii...and thus their impact on Hawaiian history.
It is located in Downtown Honolulu.
Many sights to see, in Downtown Honolulu area.
And it is not located far from Waikiki.

I have been to Oahu twice and both times we visited the Polynesian Cultural Center and loved it! Yes...it is expensive, but so is everything on the face of the planet in Hawaii. You'll pay $15 for a bottle of sunscreen over there! I do think the Polynesian Center has something for everyone and the shows we saw were amazing. Very entertaining and it really makes you feel like you have been taken away from the baloney that we encounter on the mainland and placed into a different world with great history and eye-catching talents that each island nationality will display. I think there are things that the three year old might get a kick out of at this place but it will be a long day and you are also outside in the heat and humidity so I can also see the toddler getting exhausted and having to take a break at some point. Have a comfy stroller with you because there is a lot of walking and if a nap is necessary, you want to be able to accommodate. The beach at Waikiki is also to die for and can provide a very relaxing Oceanside retreat for the day as well. You can bounce from beach to poolside and there is plenty of places to get a drink, snacks, meals....all of it. Both times when I was in Oahu, it was just me and my husband. We do have four children but they were not with us. To me, Oahu is a place for a romantic getaway or if you take the kids, they will get the most out of it when they are older. My girls would have loved parasailing, snorkeling, hiking some of the waterfall and forest areas, or taking a surfing lesson from one of the locals. Not exactly the things a three year old would get any benefit out of. My advice to you is to maybe make this a relaxing getaway and try not to get into the tourist fray of events with such a small child. Spend time poolside, on the beach, and I would try the trip to the Polynesian Cultural Center. I think that will give you the best of both worlds and also keep your toddler calm and happy as well. Enjoy your trip! It is as beautiful as you could imagine and if you get a chance to return, leave the kids at home and live it up over there!

ETA - a bouquet of flowers for SH! I'm going to Hawaii for the 2nd time in the spring, and love love love your post!!

Original:
Be careful regarding the luau food. My sister got food poisoning when she was at one (different island than Oahu, at least.)

Can't give you other advice, but good luck!

My family and I just returned from a two week stay on Oahu. We stayed in S.H.'s hometown of Kailua. We had a fabulous time being away from Waikiki/Honolulu. You didn't mention where you are staying.

My husband travels once a quarter to Oahu and I sometimes go with him. We love Oahu...it feels like home to us. You are going to love the friendliness of the people, the beautiful landscape, weather and spirit on the island.

I am a Yes vote for going to PCC. Our kids absolutely loved it and it is among their favorite things we did. I really think you would love it...it is a very family friendly place. I think it is one of the best places for you to get a true cultural experience.

All the kids working there attend the local University and pay for their schooling by working at PCC. They come from all over the Polynesian Islands and work in the "villages" at PCC. My kids loved getting tattoos in New Zealand then walking over to Samoa for the coconut demonstration. The man is hilarious..and it was so informative. There is an awesome night show called, "Ha-The Breath of Life". It is a beautiful display of music and dance. They have a new theatre that has a gorgeous film playing..the seats move and water sprays out at you as you fly over volcanoes and through waterfalls. It is awesome!!

Try hitting alot of the local shops and restaurants...so fun. If you want specifics I can PM you...just let me know. I have a whole file folder with notes from our many stays. Ahhhhhhh....If we could, we would move there in a heartbeat. We have made so many friends there and they truly are Ohana.

Have a fabulous vacation no matter what you do.

I have been to the Polynesian Cultural Center and it is amazing. It is an all-day thing though. There are all types of luaus around, but I think anything that meets your qualifications is going to be a bit expensive. Do you know any of the locals that can advise you?

The Polynesian Cultural Center is your best bet for what you are looking
for. I wold do that.

Other fun things:
-the zoo which is right there
-certain times of year they have movies outside right there by the beach with a huge screen on Friday nights