I think you are a very strong candidate.
For a lot of the top PRIVATE schools, budget should not be a a big concern but the odd thing is that you say your EFC is $24K, which means your family’s AGI should be in the $140-160K ballpark. That also means they probably net around $100-120K. So, unless I am missing something here, taking out loans to make up $60k per year is not something I would advise.
You will be competitive for NCSU, which has a solid CS program. Are you a National Merit scholar because that can open up many more schools like Texas A&M?
If what you say is true then CalTech, Georgia Tech and CMU should all be in play. Question will be affordability.