The Ershui to Shuili branch line route offers a lot of outdoor fun. There are bike routes at Jiji and Ershui, and some nice hiking and swimming. Jiji has a small amusement park of sorts where you can play various games and a number of cafes and restaurants. There’s also the interesting indigenous species centre. Ershui has a monkey protection area and a cool ridge to climb. The final stop, Shuili has the cool Snake Kiln, kind of like a mini village built around an old fashioned kiln. There is lots of accomodation in Shuili and some in Jiji.
The Taiwan Folk Village is not too far (you can catch a bus from Changhua). This would interest any foreigners in the group as the displays of traditional architecture are excellent.
Two days you could also go up to Alishan. But spend the first day in Fenchihu, hiking, eating mountain grown food and old traditional Taiwanese snacks on the old street.
If you guys like the outdoors just rent a cabin at Longmen Campsite near Fulong Beach. In addition to the beach you can hike the Tsaoling Historic Trail over to Dali or even Daxi and then take the train back. There is also an excellent bike route nearby that runs alongside a clean river you can stop and swim in. The road runs for 10km or so and there are only a few houses along the way. At the end are gorgeous emerald rice paddies now abandoned but still with the occassional water buffalo tramping through the fields.
Also nearby are boats to take you around Turtle Island. You can stop on the island if you make reservations in advance.
For fun day trips head out to places along the Pingxi small rail line. You can get there in an hour from Taipei. At Shifen there is a magnificent waterfall and a coal mining museum. At Pingxi some really fun and easy hiking. Some of the trails take you to the top of craggy peaks and while they aren’t high they make for great photos. The final stop at Jingtong lets you explore an old coal mining settlement, a beautiful old train station, a gorgeous old wood villa from the Japanese era, and some excellent trails up the volanic like mountains. At the top of one you can even sometimes see monkeys.
You could easily make this a weekend trip if you stayed at Jiufen.
Be aware that in summer all these places will be crowded especially on the weekend. Be aware also that some of these places are empty in winter (when it’s still warm) even on a weekend.
I’m going to have to start charging for this info.