This weekend accomodation around Taichung

TLDR at the bottom.
Hello I just arrived in Taipei, Taiwan and enjoy my stay so far. I plan to go to Douliu this Saturday(11.December). Since I am there already I was thinking maybe I just use the weekend to see a bit of Taichung aswell so I just ask if there are any ways I can book something that spontaneously for a decent price. I do not wanna pay 1500 NT for a 8ppl shared room dormitory lol(good location tho). If thats what to expect when booking on so short notice that is fine aswell I will just visit Taichung another time. I am quite clueless for now. I do not really care if it is close to Taichung it should just be between Taichung and Douliu and accesible via public transport. Its just to stay for a night and leave I wont have luggage storing requirements either. I only looked on booking and agoda for now.
So any tips on where to look are much apreciated. Also even if you can not help in this case i am generally curious what generally works best for finding suitable accomodation. Thank you for your help! And if this posts violates any rules I am sorry it just is quite a spontaneous thing and I did not have time to fully immerse myself here.

TLDR: Accomodation search around Taichung 11-12 December 2021. Any tips, sources, websites etc. much appreciated. No need to be in Taichung just reasonably accessible via Public Transport.
General travel accomodation tips(not long term) also welcome.