"I travel to the US every year."
Am I understanding right that this would be more like saying "I go traveling to the US every year" as a "word for word" translation rather than "I go to the US every year" or "I travel to the US every year"? Basically, we're saying we are "doing the traveling" like we "do the shopping"? (it sounds a bit weird...)
Typically へ emphasises the movement verb and に emphasises the destination. If you were perhaps having a conversation about the fact you'll be away soon rather than where you will be, then へ might be more appropriate. e.g. "I won't be going to the party, every year around that time I travel to the US."
Both should be correct, although I also wonder if it's considered better style to use へ because you're stating the purpose of に行きます.
So it's the difference between; "I travel to the U.S. every year" being に vs "I travel (to the U.S.) every year." being へ?... Yeah, there is no clean way to really convey that in English over text. They really should either change the sentence to add the parentheses ( or possibly commas ) or they should accept に as a correct answer.