It's a 20-minute walk from Shuanglian MRT (Exit 2) to Dihua Street, but you won't be wasting your time as there are a number of stores selling traditional Chinese goods, such as dried foods, medicines and incense, in addition to the scenic value of Japanese and Qing Dynasty (1644-1911) era architecture, much of which has been preserved.
Nearby is Dadaocheng Port (marked by a full-scale model of a Qing boat), which is where you can hire a bicycle on the weekend and explore Danshui River. It's a green highway whether you head left or right, dotted with parks and pagodas and abundant bird life.
Dusk is the time to check in your bike and explore Ximending, where trends are set and tattoos inked. It's a great setting for connoisseurs of Japanese culture products and impromptu concerts by Mandopop demigods, especially on Saturday and Sunday afternoons.
If you have the time, dive into an MTV and choose from a large selection of films, moderately palatable food and drinks. Check out Monga, the 2010 film by Doze Niu that captures the feel of Wanhua district in the 1980s. Or, go to Red House Theater, built in 1908, for a drink at one of the lively and gay, literally, bars in the courtyard plaza.
The clock is ticking, the plane is booked for the next morning, and a longish MRT ride of 13 stops to Taipei Zoo awaits. It's worth it, of course, as there's a 4 km ride in a gondola up to Maokong, an ascent of 300 meters.
Observe Taipei twinkling below and then find a teashop draped in fairy lights that serves dinner, for an al fresco experience that is hard to beat.
Originally settled by mainland tea farmers from the south, there are Maokong plantation teas on offer as well as the better quality brews from Alishan and other "high mountain" resorts.
If it's after 10 pm, you will need to get a bus or taxi down from Maokong back to the MRT and downtown.
My final tip is the 24-hour bookshop on Dunhua South Road (Zhongxiao Dunhua MRT), where you can browse and read in good company to your heart's content before picking up a book for the plane home.
Yes, there's a lot you have missed, like one of the big-name temples such as Longshan or Confucius Temple, the fishing port of Danshui, Sun Yat-sen Memorial Park, Chiang Kai-shek Memorial Hall, a hike on Yangmingshan but you can always return.