Maybe another reason that Taiwan's incoming tourist numbers keeps increasing by 10% a year is that many good natural places are free to visit. Beitou Park is an example.
Beitou's hot springs and scenery is known throughout the country, but it is easy to get to right on the edge of Taipei and just about 10 minutes away from Xinbeitou Station.
Water there bubbles up at a constant temperature near 100° Celsius. The sulfuric water of the valley is a wonder to see and smell.
Though you are on the outskirts of a bustling metropolis, you can enjoy watching the water bubble and the steamy mists float up. You can pay a little to bathe in a hot spring bath.
There is also a free Beitou Hot Spring Museum. The exhibits explain that Japanese people developed this area and show the geology of the area.
The Beitou Geothermal Valley is located about a 15 minutes walk away from Xinbeitou Station. It is on the northern side of Taipei.
From the Xinbeitou MRT Station exit, walk about 15 minutes along Chungshan Rd to Beitou Hot Spring Museum (9 am to 5, closed Mondays and public holidays). Hell Valley (Beitou Geothermal Park) is a further four minutes walk (9 am to 5, closed Mondays).