Update [2010-3-29] A number of people get lost or can't find the right turn off on Pingguang Rd. The Biking Viking has a nice write up and a good photo of that turnoff.
This four hour ride is an excellent weekend morning ride that will help you get in shape for some of the harder rides outside of Taipei. It's amazing that such great riding is available so close to Taipei, and if you use the MRT, you can cut out nearly all of the unpleasant city riding. I timed this ride starting in the Yongkang St. neighborhood. If you take the MRT (recommended), your actual riding time would slightly less than 3 hours. This ride lower medium in terms of difficulty-but you must be comfortable with climbing hills. If you have not learned how to climb hills yet comfortably, I would recommend you practice on the road through the Fudekeng cemetery behind Liuzhangli. This ride is written up in Great Taipei Rides II: The Graveyard (and Beyond).
Taipei to Xindian
You have two options: take the MRT to Xindian Station or ride via the Riverside Park bike paths down to Xindian. Enter the Riverside Park bike path from Siyuan Rd. behind the Gongguan night market passing the Taipei Water Park on you way in. When you enter the park, turn left and head south toward Xindian. After a short downhill, you will pass the Baozangyan (Treasure Hill) and go under the Fuhe Bridge. Continue all the way down to the Jingmei River and follow the bike path along the Jingmei River. Exit the bike path at the Old Jingmei Bridge on Jingwen St. Cross the bridge into Xindian and go straight on Jingwen St. until you run into Roosevelt Road. Continue in the same direction (south) along Roosevelt until you get to the Xindian Station.
Exit the Xindian MRT station at the back where the buses park. Follow the street along the flood wall into the market street and then turn right to cross the Bitan Suspension Bridge. On the other side, go straight for about 50m. and find the entrance to Hanbi Road (there is a 711 at the corner).
Hanbi Road is a few blocks of typical city and then you have your first short climb. At some point Hanbi Rd. turns into Yongye Rd. You will pass a Family Mart in this fairly pleasant suburban area, and then all of a sudden you are cruising downhill into rural Taiwan. Now you are on Tanxin Rd. passing through farms and some very sleepy little villages. A few kilometers later you will come to a poorly marked juncture. Follow the road on the left going down. The higher road on the Right (Tanxin Rd.) is the one you will come down on in about 90 minutes to complete the loop.
After you take the left hand turn and go down, you will do another brief climb and then will find yourself riding beneath some pretty cliffs along the edge of the Xindian River. The water is a beautiful green on sunny days and there are lots of flowers here in the spring. Stay on this road until you come to a T-intersection with a few houses and a country store on the right. Buy water here--this could be your last chance for the next 15km, most of which will be uphill.
Pingguang Creek to Shitouzaishan
Turn right onto Pingguang Rd. Follow Pingguang Rd. along the river for seven km. You are going steadily uphill now, but the grade is very forgiving and you should be able to make good time. The turn-off to Shitouzaishan (Lion Head Mtn.) is always a bit further than I think. You are looking for a bridge just after km. 7 next to a country store made of green corrugated metal (this store is only sometimes open on the weekend). The house across from the store is No. 285 Pingguang Rd. and there is signage (all in Chinese) for Shitouzaishan, Youlai, and Jiqing Temple. Cross the bridge and begin the climb up a beautiful quiet country road. You can stop for a quick dip in the Pingguang Creek on the far side of the bridge where a rough trail leads down to the refreshing water.
The climb is about 8km and takes around 60 minutes with one 5 or 10 minute break thrown in. The first few km. are relatively tough as you gain altitude but it gets easier and there are some nice flat sections between km. 10 and 12 you can rest on. At 11.5 a small stream crosses the road. If you look to your right up the hill, you will see a 'waterfall' about 3 meters high. Alas there is no pool, but you can use the waterfall for a very refreshing shower. There is another small pool on the left that you can take a quick dip in if the water is high enough. At km. 12.5 there is a nasty straight climb that can be a bit of an unpleasant shock if you have been taking things too fast. There is a temple around km. 13.5 where you can go upstairs and help yourself to warm water and stale cookies (leave a donation) if you are really desperate. The temple caretakers are nice but very spaced out--they are Taoist practitioners who spend most of their time quelling demons.
For some reason, I have seem more people bonk on this climb (myself included) than anywhere else in Taiwan. It's not that tough of a climb, but I think people try this when they are still getting into shape and sometimes push themselves too hard. It's also usually very hot by the time you get to the top in the summer. I don't like being up here too long after 9:00am in the summer. So please make sure you bring plenty of water and some snacks for this. If do this ride in the spring, you will see flowers everywhere by the sides of the road and, in the evening, fireflies.
You will pass the entrance to the Shitouzaishan hiking trail and enjoy a nice view of the Ankeng area of Xindian around km. 15. You then enjoy a screaming downhill that never fails to surprise me by how long it lasts. You will come out on Xintan Rd. at the junction I mentioned earlier. Head back to Xindian via Xintan Rd. and Yongye Rd.