Winter is from May to October, although it is quite moderate weather. The most popular time to visit the island is May 1st until October 31st, but that means it will be extremely crowded and the prices will be expensive. During the tourist season, the rooms and everything else will be at the highest prices of the year and would be quite hard to manage on a limited amount of funds.
The best time to come visit is November 1st until April 30th which is also summer here at Tahiti, if you want to experience the island without such a crowd. If you want to have the beaches and all of the other areas a bit quieter, then the best time to come is after November. This is ideal because during this time the hotel and tour costs would go down quite a bit because it is the off season for travellers. This is also the perfect time if you are trying to visit the island on a budget and you wouldn't have to sacrifice much in order to have the best rooms.