The RCI timeshares in Waikiki are fine, but you would find a wider selection of nicer resorts on the other islands. Not sure what kind of RCI time share you are entitled to (gold crown, etc).
You do not need a car in Waikiki, but you may want to get a car for one day to explore the island. The north shore is a must - Haleiwa, Sunset Beach, Banzai Pipeline, shrimp trucks. You can also have fun one day by renting a moped. With thsi you can get to Aloha Tower Marketplace, Ala Moana Shopping, Diamond Head. Can't go on highways though.