The Lansdowne isn't that great, it's expensive and still a bit of a walk away from the stadium. The vast majority of bars and pubs in the City Centre are neutral and easy to get to. The vast majority of Bluebirds fans drink around where their old stadium was, not too far from the Cardiff City Stadium.
I'd say the best pub to use is the Prince of Wales, right by Cardiff Central train station. It's a Wetherspoons, so really cheap, easy to get to, and a short taxi/ bus ride away from the stadium itself.