I would probably use "however" in most circumstances. "Nonetheless," or "nevertheless" are fine to use, but I feel that they give one's writing a stodgier feeling. Compare this sentence taken from Wiktionary:
"She wanted to go; however, she decided against it."
Compare that to
"She wanted to go; nonetheless, she decided against it."
It's not the worst possible word choice; both are fine. However, in my opinion, the latter doesn't flow as well as the former.
A lot of it, is, however, personal preference. "Nonetheless" has its uses, but I would recommend using "however," most of the time.