I got it wrong yesterday - I thought Stoke were in the top flight in 1987, but I checked earlier and in fact they finished 8th in the Second Division. City, meanwhile, finished 13th in the Fourth Division.
We had a proper FA Cup run that season - a 4-1 win at Ton Pentre in the first round (that was a funny afternoon), a 2-0 victory over Brentford of the Third Division in round two, and an eventual 1-0 victory over Millwall of the Second Division in a second replay after the first two games had finished 0-0 and 2-2.
It was the same season we beat a First Division Chelsea side 2-1 in the League Cup.