My last visit was nearly 5 years ago so any recommendations have to be taken with a pinch of salt.
The place I enjoyed most was
The Plasterers Arms for it's eclectic range of cask and keg beers, friendly atmosphere and decent pizzas. It's just outside the city centre but an easy stroll which also goes past
The Kings Head which has a decent range but less interesting than others.
I had a thoroughly enjoyable evening in the
Fat Cat Brewery Tap which, as with most brewery taps, is a long way from being a traditional boozer and is a fair way from the city centre. The ale range though is excellent and I'd hire a bike from the station and cycle there if I was visiting again.
The most famous and renowned boozer is
The Fat Cat which has a superb range of beers and is probably the one must visit place. Also a walk from the town centre so the bike may come in useful again.
The two I visited in the city centre were
The Vine for a decent Thai but not an essential for beer and
St Andrews Brewhouse which had only recently opened, was something of a wild card and I was impressed.
It's a fantastic city with plenty to go at. Enjoy it.