Taipei

Hi Rob,
1) The National Palace Museum is the place you must go. Most of the forbidden city treasuries were shipped and stored here when the government evacuated from the Mainland.
2)You can visit Shi-Lin night market where you will find various snacks.
3)It's hard to get as low price hotel as you required. But you can try youth hostel.

Victor

Hi Rob,
1) The National Palace Museum is the place you must go. Most of the forbidden city treasuries were shipped and stored here when the government evacuated from the Mainland.
2)You can visit Shi-Lin night market where you will find various snacks.
3)It's hard to get as low price hotel as you required. But you can try youth hostel.

Victor

Hi,
Near Taipei Main Station. Many Singaporean forumers on a budget have stayed here, No frills but clean and safe. They also give you an NTD200 coupon which you can use as a discount for your next weekday stay. I think their weekend is Fri-Sat n Sun nights
Future Star - http://www.futurestarhotel.com.tw
Food MRT all nearby.

I always recommend this place: http://www.ymcataipei.org.tw/

It's a YMCA but it's not a hostel and has clean, good rooms in a very central location in your price range.

For museums, the National Palace is, of course, the best and the most famous. I also happen to like the Fine Arts museum as well as some of the smaller museums (the puppetry museum near Dihua Street is one of my favorites) and the 228 museum is very informative.

For night markets, sure, try the famous ones, but my favorites are the smaller ones. Ningxia Street, Raohe, Keelung - these are little slices of amazing. Jingmei is easy to get to, kind of grotty, very local, and I love it because it's so local.