Full-Sail is borderline degree factory, but that also depends on the major. It's known for music production and game design, apparently.
DigiPen is by far one of the best game design institutes you can go to if you are looking for something specialized in that rather than a state school.
Since it's near Microsoft and Nintendo's headquarters (though I think Nintendo moved), as well as other studios' locations, and they work closely with DigiPen, its graduates often get hired right out of graduation to work in companies. Kim Swift and her classmates got hired by Valve straight out of DigiPen to work on Portal when Valve saw their talent and ideas.
https://www.digipen.edu/
Don't go to Ai. If you're going to throw money at a school, throw it at a school that isn't
a for-profit company that's going to give you a degree that won't get you a job.
If you can't go to a specialized school, look at getting a degree in Computer Science from a reputable school and specialize in 3D programming or network infrastructure. That's a major desire for employers at game design studios.