Is it legal for a 17 yr old girl to date a 20 yr old as long as they don't have sex?

That can only be answered by looking up the laws for your state.

Go to your state's official website and find a link for state laws (it may say statutes or something like that) and search for statutes (laws) pertaining to your question.

As far as I know, in the US there are no state laws governing dating. However, any act of sexual conduct is probably defined somewhere. Your state specific laws may be different than mine. I know until the age of consent (dependent on location) you are under your parents authority. After that you may do as you wish.