Tahiti is the main hub of French Polynesia, any international flight will first go to Tahiti, any sailing vessel will stop past here sooner or later when crossing the pacific.
Hitchhiking around the island
There is only one route, basically, or thats what people say. In fact there are a few more but they go parallel and are only for a few kilometres. There is lots and lots of traffic. Around 7am to 9am and 4pm to 6pm there is traffic jams anywhere 5km around Papeete.
At these times it will take you easily an hour to go 20km simply because you are stuck in traffic.
Hitching is fairly easy. French is strongly recommended. English will do the job but be prepared that you will have strong communication difficulties.
Hitching in town is useless. Walk out of town for at least 2km. The road around the island is marked every kilometer with a marking stone, which is called "PK". (pronounce it something like PEH-KHA)
Along the way there is lots to see next to the road, sometimes its only a 15 minutes hike and you are at stunning waterfalls, etc. Go get a map at the tourist office and ask for directions. Do jump off any car whenever you get to a spot, you should be able to find a new lift quickly. After around 20km outside of Papeete hitch hiking becomes very easy and you won't wait longer than a few minutes.
Hitchhiking towards Punaauia (West coast)
Walk out of town, until the RDO starts (thats the 7km long only highway). There is a nice spot just before the "Piscine Municipale", the main swimming pool.
Hitchhiking towards Mahina (East coast)
Probably the best is going to the Shell servo (a gas station, my dear American hitchhikers). Thats on corner Avenue Prince Hinoi and Boulevard d'Alsace.
There is a hitch hiking race around the island. (no official website, no official date, etc, basically nothing official at all). They do the loop in around 3 hours. Check especially on Facebook for any information regarding this as most information is posted there... somewhere.