Are "come at" and "come over at" slang, idioms, dialectual, informal or bad English?
- If you ever visit London, come at my place.
- If you happen to be in town, come over at my shop.
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Neither of your uses are acceptable in the sentences you've written. In both, you need to use "to". I don't even think they're slang or regional.
- If you ever visit London, come to my place.
- If you ever happen to be in town, come over to my shop.
Now, there's generally nothing wrong with either "come over at" or "come at"... but you only have specific times they work... for example, if you are telling someone when to arrive:
The party is at 3 pm but if you want to help me get ready, come over at noon.
I'm telling everyone to come at 6 pm for dinner.
These are perfectly acceptable everyday usage.
One notable (?) example of a regular but slightly odd usage is the idiomatic phrase/meme made popular on the US TV show Jersey Shore.