Most things in Taiwan will not cost too much until you begin purchasing specialty items. Here is what you can expect to spend in Taichung for the following (all estimates in NT$):
Monthly Expenses 8,000 – 12,000
Chinese Meal or Lunchbox 90
Foreign meal 250
McDonald's Value Meal 160
Tea Drink 20-40
Movie 210
Cable TV 600
1l Unleaded 95 Gas 33
Bus Fare Downtown 26
Taxi Downtown 120
Practical Cellphone 600
Practical Scooter 10,000
Practical Bicycle 800
English Language Newspaper 15
In a study conducted by Mercer Human Resource Consulting, Taipei is ranked 48th in highest cost of living. In comparison to Beijing (20) and Shanghai (27), Taiwan itself is well below the expenses of major cities. Comparing costs in Taipei and Taichung, Taichung is considerably cheaper. For example, road-side meals and drinks are approximately 30% cheaper in Taichung, and shared apartments, or single-room apartments (with a bathroom but no kitchen), are 2/3rd's the price or less as well (of course actual location plays a factor in price of accommodation for both cities).
Apart from the financial aspect, there's another, maybe even more important but less definable in figures and that is the environment. Taipei is a giant metropolis with millions of people vying for available space, trying to prove to the world how modern it can be, thereby losing some of its uniquely Chinese aspects. Apart from being dramatically cheaper, life in Taichung is also much more laid back, much more traditional and less westernized.