あちこち means 'here and there' or 'various places', while そこら中 emphasizes that something is spread throughout a particular area, often with a sense of disorder or abundance.
至る所 is a more formal or literary way to say 'everywhere', whereas そこら中 is casual and colloquial.
Etymology
Compound of そこら (thereabouts, around there) + 中 (inside, throughout). The exact derivation of そこら is uncertain, but it is a colloquial demonstrative form related to そこ (there).
