Lots of the western style restaurants with a bar like Chili’s, Gordon Birsch, Friday’s are open, can those be under your category? Price might be a tid bit high, but if you need that drink and a TV with sports on at mid day, might be your only choice.
If you want a craft beer, not many places are open, but I do know that Zhang Men over at Yong Kang Street opens a bit after noon since it’s in a very touristy area.
Another option is Take Out over by Tong Hua Street night market. They primarily are a burger shop, but also serve some craft beer and have a ginormous TV for you to watch and chill.