Chaus - I'm estimating the cab fare (based on what I've paid HNL to my house) to be somewhere in the range of 40-50 dollars - depending on traffic, the part of Waikiki you are staying in, etc. There are often limos at the airport that charge the same rate as the taxis and can easily hold 6 or 7 people and luggage. Split 6 or 7 ways a taxi would still be cheaper than a city shuttle or whatever.
Instead of renting a car it is possible to get around pretty easily by using either The Bus or the tourist trolley (sorry - don't know the offical name). The tourist trollies cricle around between various tourist desitnations and let you get on and off an unlimited number of times.
Otherwise you might consider a local car rental agency - which might have better rates/options for the under 25 crowd. Split 6 ways a van might still be cheaper than a trolley. Remember that most hotels do not include parking - so there is an additional charge if you need to park the car.
A few possibilites (from the local phone book):
Paradise Rent-A-Car 946-7777 (says '18 and older welcome')
JN Car and Truck rentals - 831-2724
VIP car rentals - 488-6187
Hope this helps.