We recommend to land in Geneva (GVA) as it is 31 minutes by car from Annecy.
You will find direct flights from New York, we recommend using Air France or Swiss airline.
We recommend you to rent a car (from the Swiss side of the airport), you will be able to more freely explore the area!
The public transportation from GVA to Annecy is otherwise possible by bus (timetable here).
Another option is to land in Paris or Lyon, spend a few days there, and take the train to Annecy (book here).