I stayed at the Westin Taipei 6 times in the past 1.5 month. The service is excellent, and the rooms are nice (the hotel is <1 year old). I agree with the others that the area near the Westin is not very nice, but if you want to play tourist, you would probably take a taxi or subway anyhow.
A little sidebar. The subways in Taipei can be a little intimidating (even for someone who was born in Taipei like myself). Cab rides are relatively cheap compared to the states. You should be able to get to most places you want to be from the Westin for less than $300NT (~$10US).