If I had NMF, I would take advantage of a freebie or near freebie.
I get Rutgers is a great school with a great rep.
But it’s no different than most other flagships so if a Bama wants to send you to school for free tuition and room for four years - or others want to pay tuition. etc. I’d find it hard not to take it.
From what your folks want to pay, you could save most of it - maybe spend less than $40K in four years. So what you lose in reputation which is hard to quantify and might not pay - they’d save in hard dollars. Few have that opportunity.
Most flagships are solid and with recruiting now mostly done online - yes, they all have career fairs but most are finding jobs via indeed and linkedin, etc. - the rep of a Rutgers vs. Oklahoma State vs. a UTK vs. Alabama - it’s not worth a six figure difference - in my opinion.
I wasn’t sure you wanted a big school - but Delaware, Ohio State, Purdue, ASU, Florida, Iowa State, NC State might be others to look at but to me - they’re similar to the experience you’d get at a very find Rutgers - but again, when one is lucky enough for NMF - well, that’s a gift and you can cash in.
Kids with CS degrees will get jobs - if they pass the tests they are given by the companies.
You might see if there’s an area of CS you are interested in - and who offers that.
Good luck to you.