Just out of the parking lot (directly across from the terminal) and up a few stairs is the Le Truck stop, where you can easily get a ride into Papeete (if you don't mind carrying your bags). The fare is just around 1 dollar and 30 cents per way in comparison to at least 10 dollars in a taxi (I think it was 15 for me). Schedules vary and thin out the later it gets in the evening, but you can usually catch a ride between the airport and Papeete. (around 3 miles or so).

Ferry is reasonably priced and comfortable, though I don't remember the details. Definitely longer to do by taxi/ferry but cheaper. Can get a taxi at the Moorea dock to your hotel - but I can't remember the cost of that - nothing too prohibitive.