Maybe Yehliu or one of the beach-y areas on the north coast? That’s assuming that all the international press have left Yehliu already and things have quietened down a bit, of course. I thought Heping Island Park was “kind of okay”, too. Or a couple of the places on Yangmingshan?
I get the impression that most tourist places in Taiwan are quite good for breastfeeding rooms and stuff. Never needed to use one in a hurry, though.