Small town in Oregon here (all measured along the routes walked, not 'as the crow flies'):

• Convenience Store: ~150 meters, right down the road
• Supermarket: Will get back to later
• Bus Stop: The local bus company runs a loop around town so there's technically one closer to my house than the convenience store, but the busses that can take you to another town stop at the one ~400 meters away.
• Park: Three parks, which are ~400, ~500, and ~580 meters away respectively, though there's not much of anything at the 400 meter one but some sports fields.
• Big Supermarket: Will get back to later
• Library: ~500 meters (the 500 meter park is right across from it)
• Train Station: 29 kilometers by car to the nearest passenger rail station I can find. Without a car I'd need to walk ~400 m to the bus stop, take a $1 bus ride with the local company to Town B, then take another bus ran by this town's company, and then walk another ~480 meters because they don't have a stop at the station. Google Maps predicts that trip will take about 1 hour 20 minutes one-way, and it would cost $2 (or $4 round trip).

Now, I'm not entirely sure what separates a supermarket from a "big supermarket" in your mind, because to me all supermarkets are quite big by definition, so I'm going to explore three different trip options: one each to two supermarkets in or near my town, and one to the nearest Walmart, which I'm 100% sure should count as a "big supermarket", but which is a couple towns away.

• Supermarket A is close enough that walking to it is a viable option, which would be ~730 meters to the edge of the parking lot or ~875 meters to the front of the store. Alternatively, if I can plan the scheduling of my trip around it or I'm not picky about the timing I can walk ~100 meters to the nearest stop in the city bus loop, wait a while, and walk of right at the front.

• Supermarket B is 2.6 kilometers by foot, but a large part of that trip is walking along the side of a lightly-developed highway with no sidewalks, so I don't consider walking here a viable option. By bus it's the same 100 meters to the bus stop, wait, then directly to the storefront.

• The nearest Walmart is ~25 kilometers away by car, but the local bus company doesn't offer a direct route to that town so I have to take a bus to Town C, take the Town C Bus Company's bus to the east edge of Town D, then take Town D's bus to the Walmart on the western edge. Google Maps says this would take just over 2 hours one-way, and it would cost $2 ($4 round trip) because Town D's busses are all free to ride at the moment.