We're about 2-2.5 miles away, the track is across the intracoastal so the sound carries across the water, though we're just a couple of blocks from the ocean, so we mostly get this nice, constant rumbling of waves sound.
I live about 150-200 yards away from Boston's Green Line. I can see and hear it. My apartment is a commuter's dream, yet here we have garaged parking . The trains are more like trollies so they're very quiet and not really bothersome. Honestly the car traffic is worse... or the couple drunk college kids yelling in the streets at 3 AM.
Most days the last train runs by shortly after midnight. The first train isn't until 5AM or so. For people who sleep normal hours, this isn't too bad. I usually do hear that first train in the morning, but I black it out.
I used to take the train 5 days a week. Then my employment changed. Now I usually take the train 2x a week to one location and drive 3x a week to a different location (not easily accessible through public transit). I wish I was better at taking the train to do other things, but sometimes I just don't want to deal with the time waiting and ride stuffed-in with 1000 other people. Driving seems easier.
Here in Rochester, Trains are not used for commuting, We don't have subways, Our only mode of public transit are City Buses or Taxi's. I live less than 1/4 mile from the nearest set of tracks. The only thin Trains are used for here is to transfer scrap the local junkyard loads on a train. Inside of my house I don't hear a thing, outside my house I can hear the train every time.
About 2 miles. Close enough that I can often hear the horn at night or early in the morning, and sometimes have to stop and wait for a train to pass on the way to work. Not passenger/commuter trains though.
Nearest station is a 2 mile walk/drive away but I think the closest it gets is a mile away. Used to be real spooky actually, it's in a valley so the acoustics go nuts. If you go near the top of the valley you don't hear it moving but you do hear it's horn and it echoes all over the place.