Even though our hotel was very close to the airport, about a 10 minute boat ride, we never heard any airport noise. Airplanes fly around the island, not over it. We stayed at Le Paradis, on Motu Paahi, #16 on the Bora Bora Motu Map.
The Bora Bora airport provides a free ferry to Vaitape, the main village in Bora Bora. Your hotel will transfer you from either the airport, the ferry port, or Vaitape.
The airport in Papeete has a handy luggage checkroom (consignes a bagages) where you can store your stuff while waiting for your flight or ferry.
The best way to enjoy Bora Bora, is from one of the motu, which are islets around the main island: paahi, mute iti, mute, tapu, toopua, piti aau, tofari, ome, tevaiora.
View of Bora Bora island from our hotel on Motu Paahi: