Where should I inquire about the place to exhibit the books?
One of the tourists came to me and ask.

I can't remember what he said. I thought he wanted a room to display some books.

'Where should I inquire about the place to exhibit the books?'

↑ I'm not sure this sentence is right or not

Question

Where should I inquire about the place to exhibit the books?
One of the tourists came to me and ask.

I can't remember what he said. I thought he wanted a room to display some books.

'Where should I inquire about the place to exhibit the books?'

↑ I'm not sure this sentence is right or not

Answer

That's all correct English, except you should have said "... came to me and asked," in the past tense. What do you need help with, exactly?