I mean if you r looking for a larger city, then manchester is pretty great. From my own research (bath and manchester are also my choices), bath is a quiet town, good for studying, manchester can range from very social, to very not social, depending on what accommodation area you live in. The city life for manchester seems to be quite nice, don't think a lot of students have much to complain about it. plus the campus is near the city, but not actually in it, so its convenient but there r still a lot of "green space" if thats what you want. The few good things about bath would be the higher student satisfaction, and the better placement (tho i don't think that matters a lot for you)
hope this helps ^.^