Translation:There is a big department store in Győr too.
I have a book that states these rules:
-ban, -ben for almost all foreign countries
-n, -on, -en, -ön for Hungary itself (and some islands and lands that end with -föld) and most places in Hungary
Unless it is a town ending with
-i, -j, -m, -n, -ny, -r
those get the "normal" ben/ban
Unless the -r is -vár.
then another 180 to be again in the -on group
This of course does not cover Győrött or Pécsett and I also would not be surprised if this convoluted 4 layer rule does not have any additional exceptions. Native speakers might be able to provide the holes in the above pattern.
Győrött and Győrben are both correct for "in Győr." The -ott/-ett/-ött ending is a rare ending that only applies to a few place names (only within Hungary, as far as I know). In this course you see Pécsett and Győrött. I don't think there are any others.
A more difficult problem is that some place names taken -n (Budapesten, Szegeden, Pécsen) and others take -ban/-ben (Bécsben, Veszprémben, Győrben). There is not much logic behind which ending is used for these place names; it is something you have to memorize.
Getting it wrong will only sound a little funny, at worst. It won't cause any misunderstanding.