Honolulu's transit system goes to most places that tourists wanna get to so why rent a car. The bus is cheap and safe.
Also mopeds are a great way to get around the city.
If you happen to wish to leave the city then renting a car is your best alternative--AVIS was my choice when I went they were the cheapest I was walking distance to their office. No taxi fare.
The Circle Island Buses ..#55's go to and from Tutle Bay ..BUT once you get close to the Airport you will transfer to the #19 or #20 , ,Depending which way you come back from Turtle Bay ..
The buses in and around Honolulu were pretty good. Just pay $1 when you get on and stay on as long as you like.
UK Government take note - public transport is this easy !!!!!