For only one overnight, it will be more convenient to stay near the Taipei Main Station or MRT Ximen Station areas, both areas are fairly close to each other. The airport MRT train goes to Taipei Main Station and from there you can change train to Ximen Station or simply take a taxi.
Listing below some venues in Ximen neighboring areas, unfortunately their websites are not all in English. Never been there though, just for reference.
Massage :
https://en.morganmanspa.com/
https://www.princespa.net/
https://www.havefunspa.com/products/all/1
Sauna :
https://www.facebook.com/hans1069/
http://soi13in.url.tw/