Central Taiwan has an impressive collection of large department stores, each with food courts and dining areas in their basements. You can get your share of American (McDonald's, KFC, etc.) and pseudo-American fast food here, but this is your opportunity to try some tasty Chinese food at very budget-friendly prices.
These department store food courts are very popular with the locals because they can get a helping of good old-fashioned cooking, served quickly and cheaply. The communal dining tables can be very crowded at mealtime hours and during the weekends. Some of the menu signs are bilingual, but most of the food stalls have user-friendly photos depicting the food selections and prices for easy ordering. Just walk around to the different stalls to see what strikes your fancy.
Some of the more popular food courts are at Sogo, AsiaWorld, and Mitsukoshi. Many of the stalls serve set meals, with a bowl of soup, a main course of rice or noodles accompanied with meat and veggies, and sometimes a small (very small!) soft drink. Generally these set meals are less than 4 US dollars, and they can be quite filling and tasty. One of my all-time favorite dishes is barbeque pork chow mein. I ordered this dish several times at the Sogo food court. Its version of chow mein is not great, but it is good enough and only about $3 for a decent-sized serving. Note that "chow mein" sounds about the same in English, Cantonese (my dialect) and Mandarin (the main dialect in Taiwan). One of the AsiaWorld stalls serves a huge plate of beef and broccoli with white rice for a similar cost.