I was born and brought up in Australia yet I support Brighton... It depends who your parents support.
If I lived in Stoke, my first priority would be to move somewhere else.
I lived in Nottingham when County beat us in the play off final. I went to a couple of County games back then and they played good football, but never felt involved.I've lived in Nottingham since 1983 (more than half my life) but have only ever supported the Albion. There's something about Forest I don't like, they're a bit like Leeds, living off past glories that are no longer relevant.
Notts County are the far more friendlier club, with even better (and certainly longer) history than Forest. 45,000+ crowds 60 years ago! My brother-in-law has a Notts season ticket and I sometimes go with him, so if I was inclined to support one or the other it would be them.