USA would be the most precise, and just the "US" also works. As long as you live in the USA, you can call it America when you're talking to a fellow citizen and he will know what you mean, but if you live in Canada, Mexico, or Brazil, it's a bit confusing.
Years ago, my father and I did a canoe trip into Canadian waters of the Quetico Provicial Park, which could be accessed from the USA. On the US side there were a couple of outfitters that rented canoes and everything else you needed, and they billed canoeing in the Quetico as "The Greatest Adventure in America." You had to paddle about 10 or 15 miles to reach a portage that led into Canadian waters, and there was a Canadian Customs Agent living in a small house out in the middle of nowhere, with a check station. He was welcoming and asked where we started from, and I mentioned something about the US outfitter and how they billed this as the "The Greatest Adventure in America," and he laughed and added... "Yeah, just go to Canada."
It was a wonderful trip. We paddled 100 miles and made 25 portages and saw 1 party of 4 other guys during the entire 10 days... but that was many years ago. Last I heard the place was crowded with wall to wall canoes. But the fishing? My father used to talk about how much better the fishing was in HIS youth. We were reeling in Pike and Lake Trout one after another one afternoon, and I asked him if this was as good as the fishing he remembered. His reply was, "Son, I've never seen fishing this good before!"