You'll struggle to get in any of the pubs near the ground and they are pretty unfriendly anyway. You could drink in the ground last time I went or there are a number of good pubs near Snow Hill which is probably the best way to get there.
When we last played at The Hawthorns we went into a pub right next to the ground. Quite a large place and it had a large beer garden. Thing is a carnt remember what its called, however it is literally next to the ground.