Where would we want one in Brum? Have you used the consultation thingy to ask for one in a particular point?
I got all gung-ho about this this and contacted my councillor, but she totally annihilated me by asking me where I would want one.
... ummm .... errr .... I ride on the street?
A5127 from the city centre to Sutton Coldfield is the one that immediately springs to mind. Strategic route, fairly horrid to cycle, no sensible alternatives.
Hagley Road. Pershore Road. Selly Oak High Street (for which plans have been in the pipeline since before the bypass was built).
A41 and/or Stratford Road maybe?
Probably some stuff around the centre of town.... Moor Street? Digbeth?
I dunno. I generally ride on the road, too. But I'm a fit cyclist who manages her fear of cars. There's no shortage of places where I'd happily use segregated alternatives if they were decent. (I regularly use the new A38 cycleway; it's marginally slower than riding in the carriageway, faster at peak times, and generally less stressful. I avoid shared-use bollocks, unless it's a useful shortcut or something.)
"Look for where the BOSists are pavement cycling and build them there." is probably a good heuristic, if vague.
https://www.widenmypath.com/birmingham/ seems to be a decent project to collect grassroots suggestions. I've added a few comments there, though mostly in the classes of "This cycle facility needs fixing because..." and "Filtered permeability would be good here."