In
お店や学校や駅が近くにあります
would there be a subtle difference in meaning if 近く was used here instead of 近くに? E.g.
お店や学校や駅が近くあります
In
お店や学校や駅が近くにあります
would there be a subtle difference in meaning if 近く was used here instead of 近くに? E.g.
お店や学校や駅が近くあります
近くに and 近く as adverb mean different things. The former is near and the latter soon (temporally near).
So お店や学校や駅が近くにあります is the only possibility as in
This 近く is a noun meaning neighborhood.
近くあります is possible, meaning to happen in the near future.
I guess 近く日米首脳会談があります is better; other verbs are possible 近く日米首脳会談が行われます. This 近く is an adverb, but a bit formal and not (often) used in usual conversations.
For comparison
The former is an ordinary sentence meaning a pastry shop will open nearby. The latter is a bit stiff way of saying a pastry shop will open in the near future.
Technically ケーキ屋が近く近くにオープンします is possible, but of course, this is never used.
As per @aguijonazo's comment, only the first sentence is correct. I think your confusion comes from that 近く is both an adverb and a noun.
The adverb 近く is the adverb form of the adjective 近い, meaning "close to/near".
近く, however, is also a noun meaning "places nearby", or "the surrounding areas". A synonym in Japanese would be 付近. When you say 近くにある, that means something is nearby, or "in the proximity areas". You can also say 近くのXX or 付近のXX meaning the XX nearby.
Using the adverb 近く to modify ある is unnatural in Japanese, so you'd want to use the noun 近く, which needs a に when paired with ある to denote location.
The same goes for the antonym of 近い: 遠い. 遠く is also both an adverb of 遠く, and a noun meaning "places far way". 遠くへ行きたい would mean "I wanna go to far places", and 遠くのXX means "the XX far away".