There are three U.S. cities offering a direct flight: Honolulu, Los Angeles, and San Francisco. The flight from California takes slightly less than 8 hours. You can depart around lunchtime and arrive around dinnertime (thanks to the time difference).
The airlines that fly from the U.S. to Tahiti are Air Tahiti Nui, Air France, Air New Zealand, United, and French Bee (a French airline with good service; my family flew with them).
You’re most likely to get good weather in the dry season, from May to October. During this time average temperatures reside in the 70s and 80s, with low humidity. The drier northwestern coast will likely have plenty of sun and clear skies.
The rainy season begins in November and continues through April, with frequent showers and occasional storms. Average temperatures remain in the 70s and 80s, but humidity increases. Fortunately, during these sultry months, a breeze tends to blow from the interior mountains at night.