Good pick. Went in the Blackburne Arms years ago and wasn’t impressed but it may have improved since.
Blackburne Arms is good for food, but if you're just going for a drink you're much better off elsewhere. Also, the standard of the Blackburne Arms live music is pretty piss poor (by which I mean guy on a guitar doing Oasis covers).
Peter K's will always be the best pub for me. I think Ye Cracke and the Grapes are the next best. Caledonia, Belvedere, The Cambridge, Roscoe Head, and yes even the little sweaty mosher/student den known as the Pilgrim, are also good options.
I've never been that taken by the Phil.