I think mathematical logic is potentially a bit of a red herring. I could imagine it's easy to think, "I want to practice thinking logically, surely a good star

I think mathematical logic is potentially a bit of a red herring. I could imagine it's easy to think, "I want to practice thinking logically, surely a good starting place is... logic?" But actually I don't think necessarily involves any more creative thinking or problem solving than any other area of mathematics, and is perhaps hard to appreciate until you've practiced mathematical logic less formally. I'd suggest something like linear algebra or analysis (in the mathematical sense of formal proofs in calculus). Those are both a bit higher level than logic, but still very abstract.