'giving me a tour of' is correct and usable in written English. You can use it when you want to explain that someone is taking you on a tour of a certain place. For example: My uncle is in town and he's offering to give me a tour of the city.
He began by giving me a tour of the kitchens.
(You can also watch a video of Alissa giving me a tour of the streets).
I'd managed to talk Robinson into giving me a tour of his family's island.
Before giving me a tour of the house, Murphy unpacked a box of small black rubber circles.
He shakes my hand and offers to give me a tour of the hostel, where he arrived a week ago.
Nash gave me a tour of the pumping station.
He gave me a tour of the settlement.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union