Rent: In Taipei, $16,000+; in rural areas, you can find a good place around $6,000
Food, travel: I generally spent ~$8,000, but I ate out frequently (pretty normal there.) If you stick to mostly 7-11 food and don't eat much you can bring this down to 4,000. Food is also more expensive in Taipei than in surrounding areas.
Public transportation is excellent and cheap, there's little need to get your own car. A bike or scooter works great.
Total:
$24k ($720 USD) in Taipei
$14k ($420 USD) in rural areas (i.e. Yilan)
$10k ($300 USD) will get you by if you're really on a budget
Quality of life is very good for foreigners. The people are very friendly, and can speak enough English for you to get by (although speaking Mandarin is a plus.) You've got your standard McDonald's/TGI Friday's/Burger King/Subway/other American establishments if you miss them. Being an island, it is very humid and does get quite hot in the summer.
Also, the entire city of Taipei has really cheap wifi! A couple bucks a month gets you internet access from anywhere in the city.