What is the difference between soba and chikaku
They're very similar. I think you could say that "soba" has more of a feeling of "by / next to", and "chikaku" is more "near / in the vicinity".
Why does this use 'に' rather than 'で’?
The particle に is used to show location whereas the particle で shows location of where something happens. Since this sentence is only telling where the post office is, に is used.