My favorite coffee shop on Oahu is Morning Brew in Kailua. They make a wonderfully flavored latte and a delicious bowl of oatmeal, too.
The atmosphere is lively, but warm and comfortable. Wi-Fi makes it easy to peck out an email back home, or catch up on a little work.
In the evenings they occasionally have live music and serve wine with their meals.
The food is delicious - very fresh. And the desserts... well, you will just have to check those out on your own...