I was actually thinking of Birmingham as the third, not Edinburgh - Edinburgh Zoo is further from the city centre than one would think, certainly further than somewhere like Chester Zoo which is definitely not an urban collection, and Belfast which I am given to understand is also located on the city fringes.
To some degree it is a case of city zoos having closed down - look at Manchester, Glasgow and Cardiff for instance - but there are definitely a surprising number of cities which have never been well-served where zoos are concerned

Newcastle for instance.