It is going to depend on the likely local knowledge of the person asking. If someone asks and we are in my county or a neighbouring county, I'll given my village, but if I was hundreds of miles from home, I would say the nearest town, which isn't far out as I only live a mile from the edge.
If someone where I live now asks where I am from, I say Salford, which has, once or twice, got the reply "oh, Manchester", to which I say "No, Salford". Salford is not part of the city of Manchester. Some might accuse me of pedantry but I don't care. You wouldn't say a person living in Scotland lives in England just because Scotland and England are next to each other and part of the UK.