I would think it would depend on where you lived and what you wanted to do.
If you live in a very remote place where your nearest neighbour is 4 miles away and the nearest supermarket 20 and hospital 40 miles away, the definition of local is different from where I am where you can walk for miles on footpaths around the village, have a choice of three shopping towns, all 4 - 5 miles away, but need to go 15 miles to the hospital. In a city where the nearest green space is a mile away, the supermarket down the road and hospital 2 miles away, the definition is different again.
On a bike I would consider 7 miles local, providing the cyclist cycled there and back.