Yes, this question was asked and answered on this site 3 years ago, newbie! 
I’ll try to be a little more helpful than Juba, though.
Here’s the thread from last year on this subject:
[forumosa.com/taiwan/viewtopic.ph … tel#165789](Hostels in Taichung-info greatly appreciated
As with most cities in Taiwan, there are several budget hotels located within short walking distance of the train station.