#sorry OP I can see that you've already been informed on the 'Tim is a Bristol suburbs brat' fanon in the replies/comments!

[umbrellacam]

Tim actually didn't move to Bristol, and specifically next door to Wayne Manor, until after he became Robin and his dad woke up from his coma. It was suggested by Alfred as a way for Tim to continue secretly being Robin, and fun fact, a secret tunnel was built under a cistern in the Drakes' cellar all the way to the Batcave to further enable his vigilante career c:

As far as we've been told, Tim grew up in various apartments/condos that the Drakes owned mostly on Gotham City island proper, and Jack didn't even want to move out of the city but had to be persuaded (links on Tim's childhood living situations: (1) and (2))

(also Steph is from the suburbs on the mainland, not Gotham City Island (or Crime Alley).)

There's not a single thing you could say to convince me that Bruce and Tim are gothamites. Look at this fucking map

Bristol is so far removed from the heart of Gotham that there's quite literally no way it shares many, if any, cultural traits with Gotham. That's not even counting the insane wealth disparity that makes the ways of life (and therefore culture and habits and dialects and food) completely incomparable. Tim and Bruce aren't gothamites, they're Bristol brats, and I fully believe nobody in Gotham would accept them calling themselves gothamites. Especially with the size of the Wayne Estate.