I would have thought that St Davids is just such a place. The entrance is challenging for buggy and baby carrier users (as it must be for those in a wheelchair too I imagine). Still, if you don't think that works then why not open one?

There is also Mr Lawrence, in Crofton Park, which is a positively child un-friendly wine bar (am talking about during the day BTW). Mind you, he can afford to be picky. I don't reckon many new businesses could do that, locally, as it would be flying in the face of the local market demographic. YMMV.