If you want a Google map with all of these spots, you can check it out here.

O'ahu

Near Honolulu, as it is the most populous city on the Island:

• Uncle Clay's House of Pure Aloha - This is one of the few reasons to go to O'ahu. It is the best shave ice on the island.
• Ono Seafood - honestly, most locations that we've been too in Hawaii have god seafood. So just check for highlight rated seafood near you and you'll probably find something.
• Liliha Bakery (they have multiple spots) - their puffs were good
• Iolani Palace - recommend going here to learn about the history of Hawaii
• Diamond Head Crater Trailhead - iconic views of the city from here
• Puʻu ʻUalakaʻa State Wayside

East-ish side of the island:

• Lānaʻi Lookout - some beautiful views
• Halona Blowhole Lookout - blowholes are fun to look at. And from this spot you can do a sketchy hike (walking on the highway, then jumping over a highway barrier, and climb up the face of a rock) to Koko Crater Arch - which is actually pretty cool to see up close.
• Makapu‘u Point Lighthouse Trail - (if I recall correctly) pretty easy walk to see the lighthouse and nice views of the ocean. Definitely recommend if you are close.
• Makapuʻu Lookout - Another place to pull over and admire the blue waters
• Kono's - I don't remember much, but I usually like bbq. :)

North of Honolulu:

• Pali Puka
• Nu‘uanu Pali Lookout - great spot to drive to and take a look
• Kualoa Regional Park

North:

• Polynesian Cultural Center - This is a popular spot. We didn't go all the way in ($$$$), we just went to the outside part where there were some shops.
• Matsumoto Shave Ice - some people say this is their favorite shave ice on the island, but that's just because they haven't been to Uncle Clay's. But if you are on the north side of the island, shave ice is still shave ice. So if the line isn't too long, it is worth getting.

Maui

Maui is a special place. Beautiful scenery and great food. I love banana bread and since they are known for their banana bread, we ended up bread from five or six different places. It was wonderful.

• Ami Ami Bar and Grill - We had a great breakfast here.
• Julia's Banana Bread - Skip the banana bread (see below) but get the dried mango. Beautiful drive if you are going to Nakalele Blowhole.
• Ululani's Hawaiian Shave Ice - Lahaina - we aren't ones to pass up a chance for shave ice.
• Haleakalā - great drive up to the mountain.
  • Haleakala National Park Summit Sunrise - breakfast on the mountain is supposed to be nice to watch the sunrise. You have to book reservations 60 days in advance.
• Grand Wailea, A Waldorf Astoria Resort - Great walking path behind the resort.
• Andaz Maui At Wailea Resort - a Concept by Hyatt - connects to the walking path, also a nice place to stay. We enjoyed the snorkeling off their beach (nothing mind blowing, just relaxing and fun).
• Mama's Fish House - this is on our list for next time

Road to Hana:

• Road to Hana audio tour - If you are doing the Road to Hana, I highly recommend picking up this audio tour. It points out potentially stopping locations and gives you some of the history. It is really well done.
• Aunty Sandy's Banana Bread - This is the best banana bread on the island. If you are doing the road to Hana, you should stop here.
• Coconut Glen's - Really good ice cream made with coconut milk. We had passion fruit and it was a delecious addition to our drive.
• Kahanu Garden, National Tropical Botanical Garden
• Black Sand Beach - First time I saw black sand. It was a fun stop.
• Pīpīwai Trail - beautiful trail at the end of Road to Hana. Really worth the walk after a long drive.

Please check out other cities!