Taipei is an enormous city with things in nearly every price range, but for most tourists it might appear to be on the expensive side, at least compared to mainland China, though certainly cheaper than Japan. It’s also quite a bit more expensive than the rest of Taiwan, so those touring the island can find reasonable bargains at their other stops.
Hotels and hostels in Taipei are of reasonable value, and standards tend to be fairly high, even at most of the places near the lower end of the spectrum. Food and drinks also come in a wide spectrum on the price scale, with famous street food and casual eats at amazingly low prices considering the quality. However, finding restaurants with English language menus in the lower price ranges is extremely challenging.
The main attractions are reasonably priced compared to similar offerings elsewhere, so it’s possible to get by on very little once you arrive if your budget is tight. Using public transportation also cuts way down on costs, so even backpackers can manage Taipei if they can find a good hostel or cheap hotel.