If Mad Max was still here, he'd probably recommend you Kozy's, The ales not too expensive, and the place is full of 'characters'!
Traditional Scouse pubs (if there is such a thing, as it's quite a wide ranging subject). - Pen and Wig, The Croc, White Star(to a point), Shenannigans(Yeah, it's an Irish pub, but it has a good mix of people), Vauxhall Vaults, The Richmond, The Beehive, ..... and then any one of about 6-8 around Great Charlotte street, and the bottom of Mount pleasant, and Renshaw street. All normal boozers that haven't yet been gentrified, and can still be a bit rough and ready at times.