Only the second one makes sense. But, "I have to go to the University" sounds like you are being forced to go. Maybe you mean "I am going to go to (or going to attend) the University."

'To' indicates movement from one place to another. When there is movement - eg with a verb such as 'go' - you use 'to'. If you are 'static' - eg with a verb such as 'live' - you use 'at' or 'in'. I go to school. I walk to school. I am at school. I study at school.