One of my favorite hikes on Oahu was hiking Makapu'u Point trail on the southeastern coast. If you're traveling around the island, from Honolulu it's just past Hanauma Bay off of Rt 72. There's a long road where you can park your car to start the 2 mile round trip hike. We tried to hike the trail on our way to the North Shore where we spent a night, but we could not find a parking space in the afternoon. I'd recommend getting there early. On our last day on Oahu we had an afternoon flight to Hilo, so we stopped on our way back from the North Shore and were lucky to find a spot just as someone else was driving off.
Although it's a relatively short hike (2 miles paved), there is a 500 foot gain in elevation, so wear proper footwear. There are no facilities, so "go" before you go. Also, there's no shade and it is HOT, so wear plenty of sunscreen and pack some water. Maybe wear a hat too. Sunburn on your scalp is the worst!
The views of the coast were amazing as we hiked along. On a clear day you can see the islands of Lana'i and Moloka'i. In the winter you may even see humpback whales which migrate to the Hawaiian islands.
The water was the most gorgeous shade of blue. I wanted to climb down and jump right in. The Makapu'u lighthouse itself is off-limits, but you get some amazing views of it from the hike. While traveling, @donvee and I like to visit lighthouses and climb them. On the East Coast in the US, I'm used to tall lighthouses like the black and white Cape Hattaras Lighthouse, which is 193 feet above ground. This little, squat guy was so different in comparison.
One word of caution - from what I've read the parking lot is a high theft area. So use common sense and lock your doors and don't leave any valuables in your car. We had no problems with our rentals on Oahu or the Big Island for almost 2 weeks, but better safe than sorry.
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All photos and content is my own from my own travels.