As someone who applied to colleges thinking they would do engineering and then not doing it, I would say your cousin needs to give some thought as to what type of job they may want in the future. I did my undergrad in a science and am now going back for engineering. Think about what you can do...
I'm considering getting my MS in engineering at either Mines or CU. While Mines has a great reputation for engineering, it will also cost me more to attend. Since I'll be doing a night program while working and my employer only contributes a litte toward tuition, I'd be paying for most of it...