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Sounds like that would be true if you were inside any closed surface.

Not quite: inside a closed surface you can't escape, but things can repeat.

You can avoid a coordinate, for example by choosing not to go there, or revisit another one repeatedly.

A black hole on the other hand doesn't have that: you cannot revisit old locations - attempting to do so moves you closer to the singularity.

Unless it's a spinning black hole, which contains closed timelike curves that can be reached from and can escape back to the outside universe?

None of those proposed time machines has ever turned out to be theoretically workable when the details are investigated more closely by physicists.

Kerr spacetime contains closed timelike curves inside the inner horizon. You can reach them from the outside universe, but you can't escape back out.

Also, the region inside the inner horizon of Kerr spacetime is widely considered to be not physically reasonable, not just because of the closed timelike curves, but because the inner horizon itself is unstable--there is an infinite blueshift there which, it is believed, would cause it to be destroyed by the first tiny bit of incoming matter or radiation.

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