"I do not know my way around here."
I think "认识" is for things that you can see and remember, so faces, pets, layouts of buildings and rooms, and layouts of a city. You might even occasionally hear “我认识这本书”: I have seen and remember this book! Of course, you might not have read it and know what it is about(但我不知道这本书讲了什么).
I do not know my way around here should be able to translate into 我不认识这里。The sentence does not specify street and I don't believe the translation should require one either. It could be 我不认识这个地方, which would work better as, since the sentence is vague, the translation should be too.