The prepositions "at", "by", "beside", and "next to" are all prepositions of location, and all relate to nearness. The choice often depends on the words that follow and the exact spatial pattern you are trying to describe.
"next to" is the most general-purpose of the group. It indicates that things or people are quite close laterally -- from right to left. Any person or thing ca
1) The ball is at the box. (x) The ball is in the box.(o) The ball is on the box. (o) "At" in the locative phrase usually means "at a point". "On X" is "touched to the surface of X".
To reiterate what I said at the beginning, I find at the box odd, or perhaps I should say, an uncommon means of locating the ball. As things get bigger and farther away, it is more reasonable for them to become a point location: I therefore find at the wall and then at the river increasingly reasonable, with Pa's boat is down at the river quite natural.