Rent a car - you will want to drive not only to Waikiki, but also to The Dole Plantation and Turtle Bay. This KoOlina Marriott is one of the most beautiful properties we have visited. You will love it!
There is a bus company called The Bus which operates a rather extensive bus network on the island of O'ahu. From the Marriott at K'olina, walk out the drive way to Rt 93 (aka Farrington Highway) and you'd find bus stops. The most convenient route for you to take to Wikiki is Route C, which is an express service. But you can also take route 93 which is the milk run version of Route C. Routes 401 and 402 will take you as far as Ala Moana, not quite to Wikiki. There's also PH1 which takes you as far as Pearl Harbor. The buses are clean and safe, but definitely not as fast as driving a rental car. You can view route maps and time tables at www.thebus.org. Good luck!
Ko Olina is one of my favorite resorts but I would never dream of staying there without renting a car. It is just too far away from everything - that isolation makes it nice and relaxing, but unless you want to spend 100% of your time at the resort, I think you will need a car.