We stayed at LiYuan for four nights and rested very comfortably. The hotel is 3 mins to the nearest MRT station on foot, and a few more minutes to ShiDa night market. For a little more money, LiYuan arranged rides between the hotel and airport; this saved us the trouble of hunting for deals. Complimentary breakfast was provided everyday (western breakfast and taiwanese porridge). In-room wifi connection was free of charge too.
A great stay if you are looking for a cheaper yet comfortable place to stay while in Taipei.