1. Check out Leonard's.
They serve a pastry called 'Malasadas'. They are Portuguese donuts and are life changing. They are warm, fluffy, and filled with piping hot Hawaiian flavors. Choose from coconut, lilikoi, and sweet & spicy. They are super cheat (around a dollar), and they also sell cupcakes and coffee. It is unlike anything I have ever tried, and really wish I could get something similar in the Bay!
2. Go to a lookout point
I've outlined the Pali lookout, Diamond head, and the blowhole, and I highly suggest you get some nature in. I feel like I would be so unproductive if I lived there because I would never get anything done! I'd be staring out the window all day.
3. Peak into the resorts.
Even if you aren't staying there, grab a drink at their bar and browse the shops. The Moana Surfrider, the Royal Hawaiian, the Sheraton, and the Hilton Hawaiian Village are all beautiful and on the beach.
4. Hit up the Cookie Corner
The main reason I visit Oahu. The end.
Other recommendations: Eat at Side Street Inn for the BEST fried chicken of your life, catch a sunset on your lanai (and even enjoy a takeout meal there), go to the Ala Moana Mall- the largest outdoor mall in the world, and get shaved ice on the North Shore.