York has always had a reputation in psychology, right from when it opened in the 60s. I guess the campus hasn't changed all that much since then 
York is not a quiet, genteel city if that's what concerns him. It is really easy to get to from campus and is thriving, bustling and beautiful. It has one of the highest rates of students staying on to live in after graduation.
I have a stake in all these games : born in Newcastle, went to York for undergrad, and then Nottingham. All three are great but, oddly, I found Nottingham duller as a city than York : more just your standard city. It's upped its game a bit since then, though. In Newcastle , students very much live in a middle class bubble, in the Jesmond area. If he likes trips out, the countryside around York and Newcastle is fabulous.
In terms of city living and lifestyle, I'd agree with Leeds. I don't really know Birmingham but many students I teach have loved everything about it.
Has he considered Glasgow, or is that too far?