Mr Red's website links to Bob Taberner's website (& other listing sites) which cover Lichfield, I believe there is Kulture in Tamworth but it may be hard to find.

The North Staffs website lists a few too in Uttoxeter(pronounced Uchester), Eccleshall, & the Gamecock in Polesworth though don't expect to be served quickly at the bar, particularly if you are dressed in a rather eye-catching colour (inc cowboy hat).

The radio Shropshire website is a useful resource too. Sunday night prog covers Heref, Worcs, Staffs, WM etc.

There used to be a session alternating with Birmingham - not sure is it still exists.