The best price found from United States to Turks & Caicos is on January 27th, 2019, travelling with American Airlines. See more options, compare prices and book: search flights.
The departure tax of US$20 is included in the price of a ticket.
While there are two other nominally international airports in TCI, you will certainly come through Providenciales International Airport (PLS). From there you can fly to the UK, US, Canada, the Bahamas, Antigua, Cuba, Jamaica, the Dominican Republic, Haiti and Puerto Rico. To get to elsewhere in the region, you'll have to transit, most probably through Miami or possibly Fort Lauderdale.