Have you visited any of these places? Anywhere you can study medicine is a good university. So I would really recommend having a think about what kind of place you would like to live and visiting them all. and making your decision based on that. I've lived in Liverpool and Leeds, and visited the other two. In my experience, Liverpool was by far the best place to live for me - in terms of its independent bars, cafes and restaurants, nightlife, culture, parks, and political history and shared views etc.
No disrespect to the other places, but Cardiff and Plymouth and even Leeds felt like they had a little less of this to me. But other things may be more important to you... shopping.. closeness to a beach... nice countryside... welsh culture... etc, which could make one of those preferable for you.