For a true cultural experience this place is where to go. Spend the day exploring all the villages around Polynesia to learn about different cultures and people. While the night show HA Breath of Life may seem expensive it is definitely worth the cost. If you are wanting to experience a luau this would be the place to combine with the show.
More steep climbing (Hawaii mountains for you). This hike leads to two WWII Pillboxes with great views of the windward side of Oahu. Please be careful as you park along the road. Follow no parking signs and make sure you are facing the proper direction or you may get a ticket... Then please be respectful as you walk through the neighborhood. Growing up we would often hike and then walk down to Lanikai Beach to cool off.
If you want to get into the hustle and bustle Waikiki is the place to be. The best bet would be to park at the Honolulu Zoo parking lot and either walk to the beach or walk the main road all through Waikiki. Parking can seem $$ so if you want to try and get free parking but about an extra walk you can try park in the Waikiki Shell Parking lot.
Another breakfast place. Expect long lines and good food. The tourists have found out about this place but locals are still willing to wait every so often for a treat. The Macadamnia nut pancakes are their speciality.