Currency rate is about S$1 = NT$20.
At Taipei, you can go to Shihlin Night Market where you can find snacks and fried chicken cutlet at NT$20, maybe you can get imitation fashion wears from the street vendors that run at the sight of police.
At Raohe Night Market, you can try the various stewed soups and grilled sotong. Plenty of unqiue fashion wears and shoes and mobile phone accessories available.
At Tonghua Night Market, it's a food and snack haven for people who love to eat non-stop.
Lastly at HuaXi Night Market, you will find exotic food like monkey brain, fried scorpions and stuff like that. Don't try the seafood here cos very expensive. In this market, you can also find erotic shops selling sex toys like full bodied blown-up dummies, vibrators of different shapes and sizes, don't be surprised to find the salesgirls cladded in translucent night gowns and lingeries. Snakes are common sight here when you can have a sip of snake blood for NT$100 which rumoured to boost your sexual performance.
In Taipei, you can also take the MTR to Tanshui where you can tour the old colonial Dutch buildings, have relaxing tea in the themed shops, get some souvenirs and taste the famous Ah Po Braised Eggs and Bah Wan (meat puffs), take a stroll down to the Tanshui Old Street and enjoy the old days of Taiwan.
There's a zoo at the end of Mucha line, but me didn't enjoyed it.
Movie watching there is rather expensive at about NT$295 (roughly S$14.50), shopping there is also a delight, you can go to Song Shou Road where there's New York! New York!, Mitshikoshi Department Store, Warner Movie Village and the Taipei World Trade Centre.
Taipei has a red light district at Linshen North Road, where pubs and karaokes are prevalent. If you are a tourist looking for sexual favours, there are plenty shops of "Gua Yang Tou Mai Gou Rou" (black shops). They can be identified by the dark tinted window panels of the shops. Make sure to check for your personal belongings after "enjoying" their services. Massage parlours are plenty here where you can ask for "special services" by pretty hostesses.
If not, you can go to shop around their equivalent of our Orchard Road, ZhongXiao East Road, where you can find famous brands like Armani, Versace, Gucci, Prada, Burberry, Chanel, Polo Ralph along the high class street in Sect 4. Along Sect 2 to 3, you can find Sogo, Tower Records and eatery shops like Ajisen and TGIF and Swensen restaurants.
If you like quiet and serene areas, you can go to Keelung by taking a train where you can find the famous Fisherman's Wharfs to eat cheap and fresh seafood. If not, you can also go to Jiufen to enjoy the half mountain scenics and taste the famous Taiwan's Dongding Oolung Tea. Otherwise, you can take a trip up the famous Yangming Mountain to try the saunas and springs, just be careful when you ask for "special services" there, you will get "more" than you bargain. For safer side, you can go to Peitou to try the sulphur springs there.
It's all depending on your likings to decide where you want to go. Just bring along about S$400 to S$500 (roughly about NT$8000 to NT$10000) would be more than enough.