noun
Refers to a general area or the vicinity of a place. Often used with この, その, あの, or after a place name.
この辺に郵便局はありますか。
Is there a post office around here?
駅の辺で待ち合わせよう。
Let's meet near the station.
noun
Mathematical or geometric use for the side or edge of a shape. Also used in some compound words.
三角形の三つの辺の長さを測る。
Measure the lengths of the three sides of the triangle.
noun
Used in set expressions like その辺 (in that respect) or この辺で (at this point). Not freely productive.
その辺の事情はよくわからない。
I don't know much about the circumstances around that.
この辺で終わりにしましょう。
Let's call it a day at this point.
近所 refers specifically to a neighborhood or the immediate vicinity of a residence, while 辺 is a broader, more general term for an area.
側 means 'side' in a spatial or positional sense (e.g., 右側), whereas 辺 is used for the side of a geometric figure or in set phrases.
The kanji 辺 originally meant 'boundary' or 'edge' in Chinese. In Japanese, it developed the extended meaning of 'vicinity' or 'area' through the idea of the surrounding region.