Poagao,
You are down in Taoyuan then? Awesome! There is such a fantastic availibility of kick-butt, eye- popping excursions down here I don’t even know where to begin!
I’ll give you two: Hmm…from your place?
First a short one. First we need to get off the flats. Probably would suggest Sanshia as access via Inge to get there. From Sanshia up to San-ming (about 16k) That will hook you up with highway 7 (northern-cross island highway) From there you will continue on up past Fushing-shan, past the two large bridges, and then to the official entrance to the northern cross-island highway. At this point you’ll see a cop shop and a gate. You’ll also see a road to your right (highway 118) take it and it’s a really nice, well paved twisty bit of heaven around the back of Shrmen dam. It runs about 40K and ends up in Hsinchu County in the town of Kuanshi. Since it runs right into highway 3, it’s a no brainer back to your place. Figure about 4 hours at a good clip, but you’ll need more as the bamboo forests, mountain rivers and villages all demand a bit of exploring! For those with big bikes, this is the place to wrap them out! You’ll see many out there on weekends. It’s never congested (for now) and well worth the trip! 
For a full day tour, continue up past our previous turning point heading toward San-Baling. San Baling is about 35km from the entrance, but you’re not going all the way. After passing through a long tunnel and a really nice mountain dam, you’re going to have to keep an eye out for a turn off to your right. (It’s about 4-6k past the dam) This road winds through a fantastic scenic valley for about 20K (sorry can’t even find it on my good map, you’ll just have to ask) then goes up a series of STEEP switchbacks that will have you in first gear all the way. It climbs about 1300meters in less than 5k! Once at the top, a high ridgeback which can be very cold!, it’s an eye-popping descent back to sea level. You will see at least 2 or three cars overheated on your ride down, it’s that steep. You will pop out again on highway 3 in Nei-wan, about 10km south of Kuanshi. You’ll need a full day for this trip.
Please feel free to ask for better directions if you or anyone else is interested in doing these trips. If the timing is right, I’ll be only too happy to join you.
If you do go, let me know how many Majesties you pass on the way up 