The Bacchus is a great pub too, that's right outside the new street exit of the train station (Under the Berlington Hotel iirc...) there's huge big blue banners otuside running 20ft up the building, through there, down the stairs with the murials on the wall, and you're into the Bacchus.
As mentioned, Wellington, Old Joint Stock, Post Office vaults are also good.
A bit further out you have brewdog, which is a top pub too and even further out you have Old Contemptables and Pub Du Vin, which are nice - these are by snow hill station, a 10 minute walk from New Street.
Within Brindley Place (canals) you have a few pubs there too, like Pitcher and Piano (mentioned above) and a few other little bars.