Sydney has Australia's busiest airport, and domestic flights, many operated by Regional Express (REX) radiate out to numerous NSW airports.
Trains reach many towns in northern and central NSW, and there's a line out west to Broken Hill and onwards.
Bus services may not be frequent, but they are reliable and cover most of the places that you can't reach by train.
The best price found from United States to New South Wales is on December 8th, 2018, travelling with Alaska Airlines. See more options, compare prices and book: search flights.