Is it legal for a 17-year-old girl and a 21-year-old guy to date in Georgia without any laws being broken?

There are no laws regarding dating in any state. There are laws regarding contact sexual with a minor. They are two different things. However, since she is a minor, her parents get to determine who she is and isn't allowed to have contact with. If her parents are okay with the two dating, then fine. But if they say she can't date him, then she can't.