i just came back from taiwan last week.
For good service, i recommend QILIN Hotel. At Kangding Road, around 10 mins walk to Ximenting. Restaurant there serves cheap yet delicious food.
Sightseeing, can go to the Martyr's Shrine, Chiang Kai Shek Memorial, Sun Yat Sen memorial. All these places are very near ximenting. Can take train. For more scenic places like Jiufen, either u go yourself or follow a tour group. Mine was a one-day tour, followed by four days OTOT. I paid around 820 for air ticket plus accomodation. Non-peak periods should be cheaper.
As for nightlife. I tell you it's nothing like you've ever seen in Singapore. WILD. Girls there are super friendly, not like the stuck-up beetches you get in Singapore. LUXY at zhongxiao East RD is their equivalent of our Zouk. Bottle of heineken is 200 NT. But cover is quite steep. Around SGD$30. But if you're not the shy type, it's a night you won't forget. There's also the famous ROXXY chain of clubs, around JINSHAN South road Section 1. Only open on fridays and saturdays. But don't go too early. The club gets packed only after 3 am and goes on until 730 am. Drinks are at 160 NT. The last time i went, it was full of taiwanese girls, and caucasian guys. Ratio around 1 guy to 4 girls. NOT KIDDING. There's Roxxy VIBE, LIVE, and 99. Got to know one of the waitresses there that night and she sent me back to my hotel on her scooter.

Then, there's the "COMBAT ZONE". Shuangcheng street. If im not wrong nearest mrt is beiquan west rd. Similar to our Joo Chiat/Boat Quay. Beware of this pub-MIAMI. Girls inside are super super burning hot. But it's a "talking bar" which means you can get cozy with a waitress of your choice on the sofa. but you have to buy her a drink which is 400 NT a glass. If you have the money, go ahead. If not the whole stretch has tons of pubs for you to have fun at. I have a favourite one, but i'm not gonna share here. LOL. Drinks are around 100 NT a bottle. Oh. And one more thing. Most of the pubs at shuangcheng st do not close as long as there is a single paying customer. I partied until 830 am. Exact address is Shuangcheng street, lane 32.
There. Hope this helps. HAVE FUN!