Unfortunately, you can't drive the complete way around Oahu. Kaena Point in the northwest isn't passable by car, and unless you're with the military, you have fat chance of driving through the Kolekole Pass from Central Oahu to the Leeward Coast. But you can drive a circular (well, oval) 96 mile course that traverses much of the island.
Drive around Oahu; follow the thick blue line
I've driven the circuit nine times and each round I've discovered a special something: a lava rock pool, a food truck, a waterfall, a snippet of local history, a vantage point, a free cup of Kona coffee, a walking trail, a cultural festival, a second-hand book stall.
For no particular reason, the following itinerary begins in Honolulu and progresses in an anti-clockwise direction.
To exit Honolulu, take the [H1] East. Alternatively, drive east along Kalakaua Avenue and circle Hawaii's most famous landmark, Diamond Head Crater. The trail to the Diamond Head State Monument offers spectacular views of Waikiki, but walk this another day; today's road trip is about exploring what you can't see from Waikiki. Soon the [H1] becomes the Kalanianaole Highway , and you'll pass several beach parks on your way to Koko Head and the incredibly busy, albeit beautiful, Hanauma Bay.
As a morning constitutional, climb the steep trail up the Koko Head Crater, or hike the coastal trail from Hanauma Bay to the Halona Blowhole. Take a breather at Koko Crater Botanical Garden, or at Sandy Beach Park, where body surfers and boarders roll inside waves, the experts miraculously pop out the ends unscathed.
Stroll through Waimea Valley or one of the Honolulu Botanic Gardens
As you continue along the  you'll move into the Windward Coast. This is the place to watch the sunrise and to kitesurf. The coastline between Koko Head and Waimanalo Bay is dramatic. Pause at the lookouts and at the beach parks to capture the scenes in your mind's eye, or on your electronic devices. In winter (December to March) look out for humpback whales. About here you can hike to the lighthouse at Makapu'u Point, or you can swim with dolphins at Sea Life Park Hawaii.
Ten minutes after you pass the township of Waimanalo, turn right onto Kailua Road; this will lead you to the pretty Kailua Beach Park. The Nuuanu Pali Lookout on the Pali Highway  offers spectacular views of the Windward Coast, but the  will have you heading back to Honolulu. The roads you want to continue around Oahu are the Kahekili Highway or the Kamehameha Highway. The latter follows the coastline, but first take the Kahekili Highway so you can pause at the tranquil and lush Valley of the Temples; there you'll find a charming Japanese Buddhist temple called Byodo-In.
The charming Byodo-In Temple in the tranquil and lush Valley of the Temples
A little way along, the Kahekili Highway joins the Kamehameha Highway. As you wind along the highway, with the Koolau Range to your left and the Pacific Ocean to your right, you'll pass beach parks, headlands, and hiking trails that beg to be explored. Other attractions here, before you reach the North Shore, are Kualoa Ranch, the Polynesian Cultural Center, and the shrimp trucks at Kahuku.
The North Shore is famous for its seven miles of coastline that is jam packed with world-class waves. This stretch of coastline begins shortly after Turtle Bay Resort. If you are driving around Oahu in the winter when the ocean is wild, then stop at Sunset Beach, Ehukai Beach Park (for Banzai Pipeline), or Waimea Bay to watch the world's best surfers slide and glide on the liquid mountains that pound the shore. In the summer, these same beaches are delightful places to swim, to snorkel, and to dive.
Marvel as the experts slide and glide on liquid mountains
Directly across the road from Waimea Bay is Waimea Valley, which is famous for its botanic gardens, waterfall, and cultural activities. On Thursdays, there's a farmers market where you can grab a punnet of the super food Samphire. As the Kamehameha Highway veers southeast, away from the coast, a detour off the highway will lead you to Haleiwa Town; there you can browse at the quaint galleries and boutiques, feast on delicious Thai, Mexican, Japanese, or Vegetarian cuisine, generate an ice-cream headache by slurping down the largest shaved ice treat in the world, or just giggle at the number of signs advertising products and services that are "The Original", "Hawaii's Best", and "Historic".
When you leave Haleiwa and rejoin the Kamehameha Highway, you'll drive up, up, up onto the plains of Oahu. You'll realise how high you've climbed when your ears pop. Peer in the rear-view mirror, or better still pull over, to enjoy stunning views back over the North Shore. On the plains of Central Oahu are fields of pineapple, coffee, and sugarcane, military bases, outlet malls, and planned communities.
Visit Dole Plantation to learn about the history of the fertile plains of Central Oahu
If you have any energy at all left in your sightseeing muscles, then visit one of these attractions: Dole Plantation (home to The World's Largest Maze); Wahiawa Botanical Garden (home to a beautiful collection of orchids and other mountainous tropical foliage); Pearl Harbour (home to a memorial to that day in 1941).
When you are done, follow your nose (and the signs) to the [H2] and then the [H1], which race you back to Honolulu.