Do I need a POV when attending the 92A reclass course in Johnston, IA or is everything close by on base?

TRADOC requires all MOS schools to provide classrooms/training, meals and billeting within close walking distance, or provide transportation to training.
Camp Dodge is only 1.35 miles total from end to end, and the RTI (school) is consolidated all at the north end, with the px just another block south of that.
You should get more information from the welcome letter, or have your AGR provide you with the printable SH information from ATRRS.

You won't "need" a POV but you'll probably want one. That said it probably won't be hard to find some one who has one there.

I drilled at Fort Des Moines and did a annual training at Camp Dodge. Definitely recommend wheels.