I'm consdering taking a new job in Michigan - will I need to join a nursing union there?

No, it will depend on if you work for a health system that has bargained for nurses. I believe if you are with a health system whos nurses are unionized, you must participate, per a newer State Law. However, not all health systems in Michigan have bargained for nurses.

Some hospitals in Michigan have unions but not all.

It depends on where you work. The University of Michigan Medical Center is unionized, for example, but the hospital across town is not. Assuming you are looking in a cute care, take a look at the health systems near where you plan to live and see which are union and which are not.

I hope you can join one! They increase quality of care as well as salaries and benefits in the surrounding area :)