In the middle of Oahu Island, located between two volcanic mountain ranges and right in their central valley is Mililani. It's close to Honolulu but has its own American suburban town feel with its own attractions and amenities and is a sought after place to live. It makes a good base to explore the island from.
Staying in Mililani is a great alternative to Honolulu but with all the attractions of the city close by. You can get the most of a smaller town vibe, like popping into the farmers market for sustainable, local products or check out the local golf club while still being perfectly located for the rest of the island with its ancient sites, beaches, monuments and stunning natural wonders.
The best thing to do is to rent a car so that you can explore the island as you wish. Check out numerous beaches nearby for surfing, swimming, snorkelling and incredible sunsets, or soak up the history of Honolulu and visit Honolulu Harbor and Pearl Harbor, and see the monument and museums there.
Very close to Mililani is the beautiful Wahiawa Botanical Garden, with many diverse plants and trails to explore.
For surfers, waves are best during the winter months, for general beach goers, you might want to visit when the water is calmed, mid April to June.