The best price found from United States to Wales is on October 17th, 2015, travelling with KLM. See more options, compare prices and book: search flights.
Although Cardiff has an international airport, most overseas visitors fly into London. Five international airports service the UK's capital but Heathrow is by far the biggest, serving most of the world's major airlines. It is also the closest to Wales. Other options include Manchester, which is handy for North Wales, and Bristol and Birmingham, both close to the Welsh border.
Many of the airlines directly servicing Wales are budget operators, which means you might get a good deal if you're coming from one of the handful of destinations that they fly from.