1) Taxi is plentyful and very easy to hail in downtown Taipei. The Four Points is not in downtown Taipei, but in Chung Ho city, Taipei county, not a very good location for signtseeing IMO. As for hotels, staying near Taipei rail road station will posiiton you at the center of transportation hub - long distance buses, trains, high speed rail, and MRT are all near by. You may try to bid on Priceline for a 4-star in "west Taipei" (that is the region where Taipei train station is located) and see if you can get a 4-star hotel room with a good price. Also, "Caesar Park Taipei - Formerly Hilton Taipei" is right opposite Taipei train station, but I do not know what the rooms look like. Read reviews on tripadvisor to see if it is something you'd like.

2) For getting to Alishan and Sun Moon Lake, please get a copy of the most up-to-date "Lonely Planet:Taiwan" guidebook to read about transportation recommendations. I have not been to Alishan but have been to Sun Moon Lake. To go to Sun Moon Lake from Taipei, you'd take train to Taichung and then change to bus or taxi, see Longely Planet guide for details. Also, according to this wikitravel page, http://wikitravel.org/en/Sun_Moon_Lake , there are direct buses from Taipei to Sun Moon Lake. You do not need a guide for Sun Moon Lake. When in doubt use Taxi as a help.

3)http://wikitravel.org/en/Alishan has some info about Ali Mountain. Basically from Sun Moon Lake you'd want to go to Taichung train station to take a train to Chia-Yi train station, then get onto the Alishan Forest Railway. Notice that this Chia-Yi train station is not the station for High Speed Rail. Most of the High Speed Rail stations are located away from city center, therefore they are not at the same location as the train stations for regular train network. However, Taipei to Taichung, and Taichung to Chia-Yi, are all short distance, a luxurious express train on the regular train network will work fine.

4) If you read Lonely Planet's Taiwan guidebook and know what need to do after you get to Chia-Yi, then you do not need a tour. Also, Alishan Forest Railway was damaged last year by a tropical rain storm. Some parts of the forest railway are still closed. Read the wikitravel page for info and then check with your hotel concierge in Taipei for up-to-date change.

Thank you for the detail response, it was very helpful. After reading more from Fodor I would like to spend 1 day in Taroko Gorge. This would make things more complicated. Anyone know of any transportable from Alishan to Taroko Gorge ?

I believe you could hire a car and driver to take you from Alishan to Taroko - it's supposed to be a beautiful, but somewhat perilous (twisty, rock slides) road.

The weather on Alishan is not predictable. I don't know the latest condition of the little train that goes there, ie is it operative? Most people spend the night at a small lodge on the mountain, get up at 3:00 or 4:00 am and hike up to watch the sunrise. I think you need a reservation for this lodge, so plan ahead.

Sun Moon Lake is actually not my top destination in Taiwan. I've nothing against it. The lake is a pretty color, and the surrounding countryside is lovely, so I'm not ruling it out...but I think Taroko is spectacular.

Stay downtown Taipei. Taxis are everywhere and inexpensive. Just take a "taxi card" with you -- your destination written in Chinese. Many drivers won't speak English. Once outside Taipei, English usage drops even more.

You can look at Edison Tours to compare prices and itineraries.