The difference between the two sentences is the use of "wouldn't" and "didn't".
"How I wish we wouldn't live so far away from the town centre" implies that the speaker believes it is possible to move closer to the town centre in the future, but they may not be able to do so due to certain circumstances.
"How I wish we didn't live so far away from the town centre" simply expresses a desire or wish that they lived closer to the town centre.
Both sentences are grammatically correct and convey a similar meaning, but the second sentence is more commonly used and sounds more natural.