The tower of Johnathon refers to two things:
1:The final dungeon in the campaign where Johnathon was the final boss; or
2:His individual tower.
Johnathon's Tower is made of a series of four towers. Each one represents a separate element, and is guarded by one of Johnathon's four generals. Lich guards the earth tower, Kary guards the fire tower, Kracken heads the water tower, and Teamut keeps the air tower. Note that the elements do not determine which element the boss uses.
Johnathon's individual tower is guarded by a shield-like barrier which can only be breached once his four generals are defeated.
Johnathon's tower is not very exciting. It is basically a long series of stairs with four rooms along the way. By entering, you see off the spirits of those fallen in the tower (pretty much enemies). There were plans to create more to this room, including a boss fight with a Epsilon from Phantasy Star, but they weren't ready in time.