I'm from Hamilton but I go to Glasgow Uni. From my experience, Hamilton isn't much of a student town, but to be honest I've never been in UWS student union. In terms of clubs you've got the Hamilton Palace just down the road and the Megabar a short taxi journey in Motherwell, neither are studenty places at all. I've a soft spot in my heart for the Palace and generally the locals exaggerate how bad it is imo. I've been to Megabar a few times and it has been okay but from what I've heard just about everyone else has been stabbed in it. Glasgow is nearby, but you're talking about a £17-£30 taxi fare in and the same out. Trains and buses before midnight are very handy though.
All in all, Hamilton isn't a bad place to live but as a local, it doesn't seem 'studenty' at all.