My antagonist vampire has to hide his face from the sun, and this is the reason why he has very long hair that reaches halfway to his hips. It suits him, hides his eyes when necessary, but maybe it is not the style you are looking for.
Didn't the late Lisa "Left Eye" Lopez of the Atlanta based hip hop group TLC wear a condom on one eye ?
Would he for sure have to cover his eyes? If he is mysterious he could just simply always have a down cast gaze. Or a habit of staring past a person when talking to them rather then look them in the eye. Fidgeting with his clothing instead of eye contact. Ect. You could even describe his eye color with words that make him more mysterious. Cloudy maybe? Things like that. Maybe even pure white eyes? Just some ideas. Don't know if they will work with your story. Hope you figure something out! Sounds pretty interesting.
Well, for a mysterious/classy character, I would say that either a bandana across his eyes, that could also cover his face (adding to the mysterious part), or he could use his own hair, if long enough. But my best bet is place a blindfold around his eyes, it's a classic way to hide eyes that I think would fit a mysterious/classy character well.
A ninja headband! Just kidding. Besides glasses, I really don't know. Perhaps a hat of some kind or a bandana? Not quite sure, since I've never really had this problem.
Since it's fantasy, you could also have his eyes just appear shadowy beneath the frame of his face, or write it so the characters are always strangely drawn away from his face, via a charm or something. Lol @ double eye patches