Hello Aussie dog,
I have only just come across your post.
The Coach and Horses in Handbridge Chester was at 17 Handbridge, just to the right as you leave Chester by the old bridge, (bottom of Bridge Street). You can see it quite clearly on Google Earth Street View. It is a bit sad looking these days. It is occupied by a company selling corporate wear and uniforms.
At the time of the 1911 census the Landlord was George H Moore, an ancestor of my Wife's. His Father was Thomas Moore who was born in Mauritius when his Father a Sergeant in the Cheshire Militia was stationed there.
The Cheshire Militia were based in the Castle in Chester and the barracks over the road where what is now The Abode hotel is built, (previously the Cheshire Police headquarters).