We are looking forward to you* coming OR we are looking forward to seeing you OR we are looking forward to your visit. I would say the first one. Laurence

I agree with James. It's more formal than some of the other suggestions but by no means would it be only used to describe some sort of monumentous occasion in the UK.

It is perfectly fine. It would not sound out of place in the UK.

Side note: the word "coming" as a verbal noun like this is usually used to talk about a big, serious event, often religious, and is not frequently used in everyday speech to talk about everyday things. The only example I can think of is "the second coming (of Jesus)". Maybe also "the coming of a new era", but a sentence like "the coming of the new neighbors" would sound strange.

It is technically correct. However a restaurant would normally replace "coming" with "visit"