Anywhere around SanYi is nice especially up to to the XinSheng Station. There are loads of beautiful hidden valleys all over Miaoli, a large part of the county being mountainous or hilly. You can drive around DaHu, SanYi, SanWan, GongGuan and just come across stuff. If you like Hakka food then Miaoli is the best spot in Taiwan to try some and there is still a strong hakka and farming culture here, not apparent immediately from the outside but spend anytime there and you will see. Miaoli is very safe and peaceful, Hakka people are generally low-key, shy almost and will almost never bother you (though some of the hordes of tourists at weekends might!).
Taian hot spring area and the entrance to ShuiBa is very scenic and some of the best hot springs in Taiwan (By the way there are no real hot-springs in GongGuan, only from DaHu up to Tai-An, but I agree the town should be by-passed by any traveller, but GongGuan township is itself nice to drive around- MM).
Flying Cow ranch is a good spot for families and adults too. TongXiao, Zaocao and the Zhunan area are nice for the hilly and coastal landscape, very different than the interior area of Miaoli, quiet places in the main and there are nice coastal/beach walks around TongXiao. You can take the train and get on and off the above places and walk around. Taiwan beer has a big brewery in Zhunan, not sure if there are tours open to the public or not. TongXiao used to have better beach facilities but they seem to have been abandoned/run-down/destroyed in typhoons.
NanZhuang is a beautiful spot, high up towards the central mountains (need a fairly decent set of wheels), this time of year is ideal to go, as other posters mentioned there is a nice aboriginal area with lake and pine forest nearby though almost always shrouded in mist it seems. Beiwan is great to catch some hakka food and drinks and get a feel of old time Taiwan (similar to Neiwan in Xinchu, which is great for looking at fireflies). I wouldn’t recommend MingDe reservoir so much but I guess to visit once may be worth it.