I'd second the idea of learning a non-Latin alphabet. Cyrillic is fun and many English speakers would only be a few hours' study away from recognising and sounding out every character. Korean is surprisingly easy to grasp and has the bonus of appearing to be quite complex. Even just plain old Greek is familiar-yet-not enough to be a challenge.

In terms of ones I personally don't know but would enjoy - Georgian script is beautiful, and Armenian looks cool too. I know enough to suggest steering clear of Arabic and Hebrew unless you're willing to commit to learning the languages themselves though. I'd be happy to be proven wrong on this though!

Knowing the alphabets themselves aren't really practical unless you're going to the country (and even then only if you can then match the sounds to some words) so it's only really a little party trick or for personal satisfaction.