What is the best way to travel from Taipei to Ali Mountain for a day trip?

Well, one day is tight for the round-trip. You can take bullet train to get to Jiayi first. It takes around an hour on the way. The train schedules are from 06:30 to 23:00. After arriving, take direct coach to the scenic area directly. The bus schedules are from 10:10, 11:40 and 13:10. The travel time is about 3 hours. In addition, the last bus return to Jiayi Bullet Train Station is scheduled at 16:40. You need to keep a watch on time.

Leo thanks! Can we make a trip via bullet train/bus to Ali Mountain spend the night then train it to Sun Moon Lake for a night then to Taroko Gorge for two nights? On day five, fly or train from Hualien to Taipei international airport for a 4pm departure to the US. Appreciate your thoughts and any specifics would be great. This would be December 9 - 13.

Yes, your time is enough, and your route is feasible. From Ali Mountain, there are only two buses going to Sun and Moon Lake at 13:00 and 14:00. If you cannot catch them, just spend one night and leave on the second day.

From the lake, there is no direct bus or train going to Taroko Gorge, so you may hire a car, and I suggest you leave on the third day.

Hualian is near Taroko Gorge, you can travel just by city bus.

Leo -- thank you for your input. Very helpful. Looking forward to a great trip, our first time to Taiwan.