Interesting question! I currently live in Norwich, UK which has been inhabited since 450 AD as a Roman settlement, and by the 11th century was the second largest city in England - so there are plenty of historical stories to tell.
I guess the 'local' stories that have fascinated me the most are the ones you can read about at the museum inside Norwich Castle, one of the town's landmarks.
The imposing fortress once served as a jail, and stories about the prisoners and their crimes can be found on display. These are the local 'horrible histories'-style stories that I find the most fascinating.
One example of the jail's fascinating history is this 'gibbet', which was used to suspend the decaying corpses of executed criminals in public places . A bit gruesome, but intriguing nonetheless!
In terms of specific stories though, I really like the one about two prisoners named Henry Kable and Susan Holmes. They were two robbers that were at Norwich Prison awaiting execution. Instead, the received clemency and were given an alternative sentence of 'transportation' to Australia (there original destination was meant to be America, but there the civil war broke out).
In Australia, they settled down, Henry became a chief constable of police and their family prospered and became very wealthy.
Since then, many of their descendants have travelled to Norwich to visit the location of their ancestors' 'lucky break'.
I like this particular story because it's a good reminder that, no matter how bleak things may seem, it only takes one lucky event for really positive change to take place, that can affect generations to come!