Closest to Waikiki:
Diamond Head Crater - Quick trail walk to stunning view spot. 
Hanauma Bay - Amazing snorkeling spot! Just bring your towel. 
Halona Blowhole - Check out the blowhole and the gorgeous views.
Manoa Waterfall Fall - Closest waterfall to Waikiki. 
Ala Moana Mall - Shop at the worlds largest open air mall. 
Pauoa Flats Trail - Good trail for a relaxing hike
Spitting Cave - Slightly challenging walk but great sunsets. 
Kewalo Boat Harbor - Many boat tours leave from here. Great sunsets.
Ala Moana Beach Park - Get your fitness walk in here. Burn calories!
Makapu‘u Point - Great nature walk to the lighthouse (45min)
SALT at Kaka'ako - After delicious food, explore all the great street art.
Chinatown/Downtown - Don't miss the first Friday of the month here. 
Queen Emma Palace - 19th-century home, now a museum with tours. 
Iolani Palace - 19th-century home of Hawaii’s last monarchs. Tours
Pearl Harbor National Memorial - Historical landmark, museum & tours.
Tantalus Lookout - Great view of Honolulu/Waikiki. Great at night too. 

Windward Side: (East Oahu):
Kailua Town/Beach - Great food, Beach & Shopping
Waimanalo Beach - Great local beach
Sea Life Park Hawaii - Dolphin experience here is amazing.
Polynesian Cultural Center - One of Oahu's top attractions. 
Lanikai Beach - Beautiful beach. Weekdays are less busy. 
Bellows Field Beach Park - Beauitful beach away from some tourists. 

Northshore:
Sunset Beach -Stunning sunsets, world class surfing, White sand beach
Banzai Beach - Best waves/surfing in Hawaii. 
Dillingham Air Field - Best for skydiving. 
3 Tables Beach - Great for snorkeling. 
Turtle Beach - Turtles come on the beach from 10am-2pm. Must see!
Haleiwa Town - Laid back surf town. 
Dole Pineapple Plantation - Like Pineapple? Don't miss this!