The Psalms Museum on Harav Kook Street displays hundreds of paintings by Moshe Tzvi Halevi Berger. The 150 psalms are each colorfully and trippily brought to life with a kabbalist sensibility in the small museum. Call ahead for tours.
While tradition attributes the Zohar - the book on which kabbalah is based - to Rabbi Shimon bar Yochai, it wasn't actually written down until Rabbi Isaac Luria - AKA the Ari or Arizal - came along. Luria is known for his work in Safed but it was in the Old City of Jerusalem that he was born in 1534. His traditionally held birthplace is now a synagogue in the Jewish Quarter. While the site may not be as famous or awe inspiring as the great Ari synagogue in Safed, (the Jerusalem one was looted and burnt in the 1936 riots) it is still considered a Jerusalem home to the kabbalah movement.
Nearby sits the magnificent Yeshivat Beit El Synagogue, for hundreds of years the center of kabbalah in Jerusalem. Since the 18th century, kabbalist scholars have called the yeshiva/synagogue their home. Make sure to check out the silver etched door depicting the seven gates of the Old Ciy on Beit El Street.
No visit to the Old City is complete without a trip to the Western Wall and the purchase of a small red string bracelet. You can usually get a few for a small donation to one of the sellers/beggars on the street. According to kabbalist tradition, the red strings protect the wearer from the evil eye, or curses. Many come with a Hamsa hand amulet, which is supposed to serve the same purpose, affording the wearer double protection.
Of course, Lag Baomer isn't Lag Baomer without a big fire. Israeli children commandeer shopping carts and snatch any wood they find in preparation. You needn't go far to find a bonfire. Just a quick stroll and you will see that on this night, Jerusalem is literally up in smoke.