Apparently Gotham and Metropolis are twin cities, literally right next to each other separated by a bridge (I think). That's not how it is in the comics, but they are making it like this in the movie to make it work. The upper class tend to stay in Metropolis while the lower class tend to stay in Gotham -- it would make sense for Bruce to have a lot of his corporate buildings in Metropolis under this idea, so it would make sense for him to be visiting Metropolis as it happened (or for him to travel to Metropolis once he hears about Superman being revealed to the world).