Star Date Online has a nice article and image about the Leonids, so named because they appear to originate in the zodiac constellation of Leo. The constellation rises in the early morning sky and dominates the eastern sky. As the Sun does not break the darkness of the morning sky until 5:30 AM, the best darkness will be from 4:00 until 5:30 at which an observer in dark skies can see dozens of meteors per hour. Another good online resources is Astronomy.com with a good article on the Leonid shower.
Image from Astronomy.com.