Cities offer larger salaries to people rather than small towns.
Here the comparison is between ‘salaries’ and ‘small towns’. The writer is saying that cities offer people large salaries and do not offer them small towns. Hmm. I would be quite happy if someone gave me a small town!
If we want to compare the salaries offered by cities with the salaries offered by small towns, then we need:
And if you really must use rather than, then you could also write:
Most of the time instead of is synonymous with rather than:
However, instead of is quite often a replacement for something that came before:
Next time make sure you’re comparing what you mean to compare!