There is a nice ride that you should try. This is the link to the Google map.
It is an out-and-back ride that starts in Changhua with a mid-point out in Nantou. In total it is about 60 km and there are a couple of climbs which makes it a little difficult. There are usually not too many cars and there are only about six stoplights total. There are plenty of places to stop for water and food, most importantly, near the top of climbs.