I don't know about Knowsley, having never been there. Twycross is probably second only to Wild Place, its definately always been one of the easiest places to get to.
Chester is far easier to get to by train than Twycross, it would be a (possible) three hour trip from New Street Station to Twycross. Chester can be done in two hours tops, both of these trips include a bus journey. Guess which one is longest...?
Never attempted Banham by public transport but it is quite out of the way, surely there must be some sort of bus to it?