"Our town is after this bridge."
Translation:Наш город находится за этим мостом.
"после" is a temporal "after".
"за" is linked to the concept of being "behind" or "following".
Here, за requires the noun to be in the Instrumental. Этот is an adjectival modifier and should agree to the noun it modifies in gender, number, and case. So it uses its masculine Instrumental form.