We stayed at Sheraton Taipei Hotel and it was perfect. Excellent breakfast buffet. French toast is very popular and there's perpetual queue in front of that counter. Easy access to all the good shopping areas. Electronics market is within walking distance (I didn't go there, but my friends did lot of shopping there and claimed that the prices of cameras & tablets were about 20% lower than in India). Shandao Train Station is nearby too if you want to use it.
Taipei is mecca for shoppers. I enjoyed shopping at following stores and markets for women's fashion:
1. New Sogo & Taipei 101 for Luxury Brands. You can find nice shoes for reasonable prices at New Sogo too.
2. Old Sogo and surrounding area for mid-range apparel, shoes and accessories.
3. Mitsukoshi - you can get instant VAT refund in the store itself on purchases of NTD3,000 or more. VAT refund can be claimed on the day of the invoice only and you'll need to present your passport. Plus there's the added convenience of submitting the VAT refund form for approval & verification at the airport before checking in. It's too much trouble for getting back 5% of the amount back, if you ask me.
4. Silk Market (i think it's WuFenPu, not sure) was the best if you want to shop for fabric for dresses, curtains, costumes... you name it, they have it. There are tailors too, in case you want to get something made immediately. Visit to the silk market was a revelation
We went to Shilin Night Market as well. It's supposed to be one of the bigger and popular night markets. I wasn't impressed. It was whole lot of junk at exorbitant prices.
All the department stores have food court, plus there are restaurants in all the shopping areas so finding food is not a problem.
If you walk into any market and foul smell hits you and makes you want to turn back and run... it's just stinky tofu. People love it here.
Sheraton offers 14 tours. We went on three half-day tours and they were all good.
1. Wulai aboriginal village tour - it included trip to wulai waterfall (it's about an hour's drive from the hotel... very beautiful), push-car ride, aborigine folk dance (it's an hour long prformance... gets interesting in the last 15 mins), stop at swallow lake for photos (lovely view).
2. Chiufen village & northeast coast tour - highlights were the drive by the coast, chiufen village market where you can get custom-made shoes, two-colored bay, and the rock formations.
3. Northern coast tour - rock formations in yehliu park were interesting.