For the Late Republic, you may want to check out this answer by u/LegalAction and u/XenophonTheAthenian - essentially, there was no such thing as a peaceful province in the Late Republic with soldiers stationed in it. The original meaning of 'province' (provincia) is much more like a 'job' (for a governor or commander) than a place, and they didn't persist if there was no need for soldiers and commanders there.

For the imperial period, when this ceased to be true, you might want to have a look at my answer here about Hadrian's Wall, which looks at the role of the many soldiers stationed in more-or-less peaceful northern Britain - primarily controlling brigandage, training themselves and local auxiliaries, monitoring the movement of people, collecting customs duties and generally being an intimidating reminder of the empire's presence.