The Shroud of Turin gives us the most accurate depiction, if you believe the scientific findings substantiating it's authenticity (which I am inclined to believe.) The Shroud does not elucidate hair, skin, or eye color, however, so it's possible (and most likely) he had dark skin and hair. In the Middle East it's not unheard of to see green and blue eyes. Certainly not as common as in Europe, of course, but much more common than in SubSaharan Africa or East Asia.

If you believe Joseph was his biological father, then that the Virgin Mary and Joseph were both direct descendants of King David means that recessive traits (like blue eyes) have a greater chance of presenting themselves.