I doubt many people stay in Taiyuan - at most they pass through on the way between Datong and Pingyao or catch a flight from there. It's true that there are more attractive places to see in Shanxi, but if you have a day to spend there, it is quite a nice city to be in.
We were catching a late afternoon flight to Shenzhen and arrived the previous day in the afternoon. We stayed at the Jinlin Oriental Hotel, 248Rmb through elong for a nice double room in a convenient location for train and long distance bus station. We arrived from Pingyao and the bus stops at a station south of the city. We caught a taxi into the centre, but got stuck in a traffic jam as police closed roads around the railway station to transport survivors from the latest coal mining accident.
On the first afternoon we went to the Shanxi Museum in Taiyuan. LP calls it 'top class' and I agree with them, at least compared to other Chinese museums. Entry is free and it is worth a couple of so hours of your time. Lots of different exhibits, and good to see after visiting the places in Shanxi such as Pingyao and Datong. Guards there were very polite as well; it must be an extremely boring job making sure people behave in a museum but they surprised us by recommending and leading us to exhibits to see - in English.
In the evening we went to 'food street' in Taiyuan, but were disappointed in the selection of places available. Nearby - Liuxiaang Nanlu is a commercial street with lots of shops and some other eating choices. We ate around there but food was only average.
The next day we went to Yuci Ancient City. You can catch bus 901 (3 rmb) from near the train station there, but while in the bus queue a taxi driver offered to take us for 20 Rmb a person in a shared taxi. Even by taxi it took an hour, so expect a long journey by bus. I highly recommend Yuci Ancient City - some parts have renovated, but it is kept extremely tidy for the film crews working there, and at least when we were there, it does not get many visitors. We had whole buildings to ourselves. There is no charge to enter the town, but there is an admission fee of 60 Rmb (half price students) for the temples and government offices - worth paying.
Near the centre of the old town are some restaurants; we had an excellent hotpot in a expensive looking place and were just charged 80 Rmb for very filling and delicious meal. From just outside the old town we caught a taxi to Taiyuan airport (40 Rmb, 30 minutes) - probably 10 or so Rmb too much.