If you want to shop and eat just like you never left the mainland this is the island to go. Waikiki has everything you would find in a mainland America mall... but just a lot closer to the beach.
I enjoy Oahu and I normally end up visiting at least for a few days during a Hawaiian trip. Mainly because it is a little more happening than the other islands and there is lots of shopping and restaurants and as a bonus you don't need to rent a car if you plan to stay in Waikiki.
Waikiki has a lot of the usual American chain restaurants including Cheesecake Factory. There are a few unique restaurants that stand out.
A few years ago I was in an athletic mode and I went on the hunt for a hike. I spoke to passenger next to me on the plane over and she recommended Koko Crater hike. This hike is not for the faint of heart... It is straight up a mountain and you are literally climbing up an old railroad track. The view from the top is stunning. Going down wasn't any easier!
During this same athletic trip, I took advantage of my jet lag and also climbed Diamond Head. Lot's of stairs. Lot's of tourists. I'm amazed when people drag their grandma's up to see the view. It was nice, but couldn't beat Koko Crater. It is a lot easier of course and definitely something I can check off my bucket list.
One thing I like about Oahu is that you don't need a car. You can be perfectly fine walking and staying in Waikiki. If you want to venture to the other side of the island you can always rent a car for a day or two. We did the drive once over to the north side and it was pretty fun. (Also to note, this is the same day that Whitney Houston died). We went to Turtle Bay resort and there are some pretty cool lookouts on the way.
I haven't ever done Pearl Harbour. One day I'll make the trek, but I have heard that it is touristy and always pretty busy. I have never wanted to take the effort to be stuck in a tour bus to go tour. Maybe next time... October 2015.
I have been to the aquarium. It is fun, but I was with kids.
At first I was not enjoying the beaches in Waikiki. I found them to be so busy with surfers and tourists. But this past trip in May 2015 changed that. The beach by the Royal Hawaiian was so beautiful, I'm now a fan.
If you stay at an SPG property, they have a shuttle that will take you from the airport to the SPG hotels. Much cheaper than taking a taxi. There is a lot of traffic in Honolulu and taxis can run you a bit of coin.
Take advantage of jet lag. Our May 2015 trip, we were up very early every morning since it was a short trip. Walking at sunrise is so calming and beautiful. Most restaurants open at 7AM.
The Sheraton Waikiki has an amazing Koi pond with rocking chairs. Perfect for relaxing in the morning.