Titan's Tower was the brainchild of Doctor Silas Stone, father to Victor Stone aka Cyborg, created as recompense for what Silas' interdimensional research did to his son. Believing that Victor would only feel at ease with other teens that weren't normal, he equipped Titan's Tower with state-of-the-art equipment. This locale eventually became not only the Teen Titan's headquarters but also an emergency base for all of Earth-One's heroes... such as during the Crisis.
The Tower of Fate was constructed by another doctor, Doctor Fate as a home for his apprentice alter ego Kent Nelson and Nelson's wife Inza. This base was constructed of bricks rather than steel, but as with the former this facility was also impregnable to most attacks from opponents. Occasionally, other heroes of Earth-Two would visit the tower including Atom and Amazing-Man (although he wasn't an ally at that point), even Earth-One's Superman.