As pointed out in the comments, ～も～も (with a positive verb) corresponds usually to the construction "both ... and ..." in English. The Japanese construction is not limited to two nouns, but one has ～も～も～も (which might be "all of ..., ... and ..." in English).
I understand the construction to be "not restrictive" in the sense that ～も～も can mean "both ... and ... and a bunch of other ...". On the other hand ～と～ suggest "exactly ... and ...". So here
Because there are no students, pubs, the city centre and everything else become quiet.
Because there are no students, particularly pubs and the city centre become quiet although everywhere else business is as usual.