There's football on at half twelve so to be sure of seeing the whole game it might be worth going Walkabout as they have multiple tellies.
Failing that, somewhere in Digbeth would likely show it as they have Irish pretensions. Would probably be a good atmosphere in there if Ireland do well. Hennesys has lots of TVs and an outside big screen, which might be okay if the weather is slightly less shit. Not technically the "right" side of town for Villa Park but neither Blose nor Coventry are at home and you'd easily make the Villa game after the rugby whether you went by taxi, train or bus.
Or you could just drink somewhere like the Aston Social but they may switch over for the football, not sure.