Taiwan visit

Rather than taking a tour, you could catch an early-morning train to Hualien, hire a taxi to take you around the sights of Taroko Gorge (or, if you are feeling adventurous and have an International Driving Permit, rent a car or scooter for the day), and then return to Taipei by train in the evening. There really isn't much of interest in Hualien itself for the short-time visitor, and the marble factory sounds like an excuse to get you to buy souvenirs. Taroko Gorge is best appreciated at your own pace!

If you have an interest in history, on your other free day, you could take the high-speed rail to Tainan, and spend the day looking around the old temples there (the Lonely Planet guide outlines a walking course for central Tainan), before catching the fast train back to Taipei.

Hello, I visited Taroko in Sept. 2009. It is worth a day trip if you have the time. I actually wish I had a week to venture the Gorge, but the One day bus tour I took was great. It will be a nice trip after spending time in Taipei. You will enjoy the time away from the city. The Tunnel of Nine turns is a great walk through. The Eternal Shrine is nice, as you can have lunch at the Cafe and view the shrine as well. As the other post says, Tainan is nice too for the history and food. Although, Taroko would get you out of the city. Have fun!

For the day you want to spend near Taipei, I like Danshui - there are some lovely historic buildings (Portuguese colonial, as well as Taiwanese) and nice views of the sea and harbour. It's easily accessible by public transit.

It goes without saying that anyone remotely interested in Chinese art should spend some time in the National Palace museum (if you're less enthusiastic, the National Museum of History might be a good choice - that way you can see the botanical gardens at the same time). The 228 Museum and memorial is worthwhile for a bit of sobering history.

Danshui makes for a good day trip from Taipei, as noted above. For the record, however, it was the Spanish (not the Portuguese) who initially colonized northern Taiwan.

Thank you all for the tips!
I'm looking forward to my visit!

You could either spend that time near Taipei or you could go down to Hualian and get a taxi to take you around. A tour would be more or less as good. All of those things are fairly short stops on the tour and can be done in a day.

But don't go by plane. It's faster, honestly, to just take a very early train there and a late train back.