Err it's really hard to stay super local when you're cycling, especially if you're reasonably fit. I can cover the distance people do for their daily walk on my bike in 5-10 mins. It's kinda why I like cycling, covers ground fast.
What's my local area? My ward? My postcode? (Couldn't take my daughter to nursery and would have to go further to go to a supermarket) My "town"? (I live in london awkwardly between towns)? My city?
To me, in zone 3 south london, quite a lot of london is my local area. I could cycle to Boris' door step in 40 mins but it 8 miles away.