My question is: is studying math at well regarded program like UIUC worth the cost, when compared with studying CS for free? It seems to me like math and CS transfer easily after college, so would the opportunities provided to me at UIUC for research, internships, etc. benefit me? I have full intentions of working in the tech industry, and I have lots of experience programming (wrote several functional language compilers in highschool, passionate about type theory, local city internship + independent study at school). I am capable of learning things on my own, and am familiar with college level courses through MIT OCW.
I love math and wouldn't be disappointed in studying it instead of CS, which I already do on my own for fun. I am not super concerned about campus attractions and lifestyle, I am confident I will find fun activities anywhere. My big concern is just the comparative value of my $$$ and time.
Go with UTDallas. They've got a great CS program, and it'll be free for you.
As another commenter noted, it really depends on what you hope to achieve in your career, but it's rare that an 18-year-old has that figured out. I'm in my late 20s and haven't figured it out!
Ultimately, the main thing Tier 1 university gives you is a foot in the door. For 95% of non-savants, the educational experience is the same, if not worse, than your "Tier 2" schools. There are many other (much cheaper!) ways to get the type of prestige which opens doors: Y Combinator, Recurse Center, an internship at a prestigious company, certifications, etc. That being said, prestige only opens the door -- you'll still need to kick it down.
Think of it this way: you are being given ~$300k to go to school. This is the same amount of money you would earn after working full-time for ~5 years after factoring in taxes. You could literally travel the world for several years and come out with less debt than paying out-of-state tuition for four years at UIUC.