We did that climb this past Christmas from the east side via Taroko Park. It's a tough climb and you may begin to regret your life halfway up.

Be aware that Road 8 west of Lishan town is permanently closed due to landslide damage so don't try to loop through there.

We liked the Rainbow Village attraction in Taichung. The National Museum of Natural Science was also excellent. On par with the New York and DC museums.