How much does University you went to really affect your chances of getting into a Grad School.

I am strongly considering just going to FIU instead of UF or CU Boulder because of the massive cost savings. Fiu would be free for me.

I right now am living in gainesville on my own, going to santa fe college, as my intention was to transfer to UF or CU. And while living on my own has been a ton of fun, I just don't know if its worth it compared to the amount of money I could save.

So I know going to a university like CU increases the chances of getting into that schools Grad School. But how much of a difference does it make? Would going to FIU and doing well, being active in clubs ect. Still give me good chances of getting into a "nicer" grad school like CU for example?