Where should I install the water softener?
Presumably you are in a non-freezing climate?

I believe that virtually all water softeners will at minimum require a shed for protection from the elements - you can't just stick one out in the weather. If that's easier than putting it in the garage, and the climate is indeed not freezing, then put up a shed and put it there. While it's remotely possible that someone makes a model designed for outside installation, it's doubtful that there would be enough volume of sales to make it economical .vs. the more ordinary inside-installation type.