Cihu Sculpture Memorial Park
Danshui
As Danshui (Dan shui) is a waterfront escape for much of Taipei it gets busy on weekends and public holidays. The area is home to several attractions. Danshui Old Street (淡水老街): lined with stalls selling local street foods and Taiwan produce. Danshui waterfront promenade: home to a mix of eateries, stalls and sideshow type games. Danshui Fisherman's Wharf (淡水漁人碼頭): offers a boardwalk, restaurants and Lovers Bridge. Fort San Domingo (Hongmao Cheng / 紅毛城): formerly controlled by the Spanish, Dutch and British is now a museum and has recently been refurbished. Bali ferry: ferry trips to the township of Bali across the Danshui River.
Jiufen
This hilly area is famed for its narrow historic lanes lined with shops selling locally produced foods, such as mochi and pineapple cakes, as well as typical street stall snack sellers, tea houses and restaurants. The area gets busy at any time of the week but especially so on weekends and public holidays. Jiufen can often be shrouded in mist, but offers some nice hillside and sea views on a clear day. Local minshu and B&B type accommodation are available.
Juming Museum
Large outdoor sculpture park created by and exhibiting the work of Ju Ming (朱銘), one of Taiwan's most noted sculptors. The mostly open air museum is located on the north coast of Taiwan. The bus ride from Taipei Fine Arts Museum passes through the scenic Yangming Shan National Park. This trip can be combined with a short trip to Yangming Shan park area or Xiao You Keng.
Wulai
Set amongst the scenic mountains south of central Taipei, Wulai is popular for its hotsprings, waterfalls and walks. The Wulai Atayal Museum is also in the area and features exhibits on Taiwan's indigenous culture.
Xiao You Keng
The sulfurous gases rising from Xiaoyoukeng fumaroles makes quite a unique site, especially so close to Taipei. Walking paths in the area offer great views, with some extended hikes possible (map boards available along trails).
Yangmingshan National Park
A natural getaway from Taipei with some nice (well signed) forest trails, waterfalls and Taipei's famous floral clock.
Yehliu Geopark
Yehliu Geopark is located on Taiwan's north-east coast, just north of the port city of Keelung. The park is famous for its quite spectacular stone formations, in particular the Queen's Head (女王頭). The Queen's Head is not expected to last too long as erosion is forecast to bring it down at some point in the coming decades due to erosion. Due to the coastal park's position, be sure to be well rugged up in the cooler months.