That depends on where you are in the US. Two states that I know of(Georgia and Louisiana) provide free tuition to all students with a certain GPA and test scores. In Louisiana the test score requirement is lower than the admissions requirement at the larger Universities, so pretty much everyone at LSU gets free tuition.

But can it run Linux?

Some people can have a lot of skill in a subject yet still be uninterested in it and perform poorly due to their lack of interest. A relative of mine had great grades in Biology in undergrad(GPA = 3.99), so her professors pushed her into medical school. She made good grades but didn't enjoy what she was doing so after 2 years and a huge amount of debt quit. She now works in the school system and loves her job.

Telling someone that they should do something solely because they are smart will end badly. Gifted student often feel an obligation to use their gifts. This is usually good. But it can cause a gifted student to persist in a career that she doesn't enjoy. So encourage your niece to achieve, but make sure she is happy with that path first.