The Eastern Catholic/Orthodox approach to visions, locutions, prophecies, and the like tends to be very skeptical. Not that we deny such things happen, but we tend to ignore (for lack of a better word) them when they do. Interestingly, this was also St. John of the Cross’s approach - influenced as he was by the Desert Fathers.
There are many prominent mystics in the Eastern traditions, but they weren’t all necessarily visionaries. Some of the more popular Orthodox mystics are St. Seraphim of Sarov, St. Theophan the Recluse, Elder Ephrem, Elder Paisios, and St. John Maximovich to name a small handful from the Byzantine tradition.
One very popular Eastern (Maronite) Catholic mystic who has a strong following even in the Roman Church is St. Charbel.