Bitan
I’ve seen some SUP there but not sure if rentals or not.
Taipei area can be challenging for SUP because basically have rivers that are dirty and variable on flow and water levels except if a few controlled areas, few lakes or not approved, and ocean area past Danshui.
Some places further away from Taipei are popular for SUP but no rentals, or but may not be located on water so need to transport. Or sometimes only have group activities not individual rentals. Some places known for SUP are Fulong, Badouzi Keelung, Dawulun Beach Keelung, Wanli, Longdong, Yehliu.