How should I greet a close friend from the United States?

You don't have to end an email the way you end a letter. It doesn't require a "complimentary closing" such as "Kind regards" or "Sincerely". Such formality seems odd in emails.

You don't even have to use your name, since the recipient already knows who wrote it.

I would suggest a single short sentence, something like:

I really hope to see you soon.

or

It was great talking with you the other day.

If you must have a complimentary closing, maybe something like a simple "Best" or "Yours" ... but I have to say, even these sound a little stilted for the format.

There are many possible answers (things that come to mind that people have used in emails to me, that I think might be suitable in your situation, include "Bye for now", "Later", "Cheers", "Ciao", or even just signing your name).

But a good rule of thumb would be to follow what your correspondent does - so for example, if she says "Regards", I'd use that too :)