Amadeus Arkham was known to have gone to college in Metropolis.
Arkham Asylum Incident
Batman found records of Amadeus Arkham relating to his time spent studying in Metropolis.
Between Arkham Asylum and Arkham City Incidents
Bruce Wayne was invited to be a keynote speaker at an event in Metropolis by the mayor. During the event he was interviewed by several reporters from the Daily Planet newspaper, a newspaper whose building could be seen standing nearby. Later at the event he ran into Talia al Ghul. The two spent the following hours reminiscing on old memories.
At some point, Hugo Strange visited Metropolis. He was there to scout for locations that would act as sites for future facilities similar to Arkham City after Arkham City's success was proven.
In Batman: Arkham City it is mentioned that a similar prison will soon be opening in Metropolis and Keystone City. In the Bowery a password in Riddler Trophy is "Metropolis" because it's maybe the Gotham-Metropolis monorail. Talia Al Ghul references having spent a night in Metropolis with Bruce.
The "Beloved" story arc in the Arkham Unhinged comic series is the first Arkhamverse story known to be set in Metropolis. The story chronicles the details of what occurred when Bruce and Talia met in Metropolis, as referenced in Arkham City.
