We are from NJ and my DD1 did NOT want to go to Rutgers (everyone I know from Middle school will be there) but was quite happy at SUNY Bing (I was happy too because it is a very good value for OOS). My DD2 thought Rutgers was too big so is thriving at TCNJ.
My suggestion is to say that you only can afford the cost of the state school (and if yours happens to be NJ, then check out TCNJ) and you won’t be signing student loans, so they need to get the net cost the same as instate. So they can pick a cheaper OOS school or apply to schools where they can get merit scholarships.
But also run the Net Price Calculator on a couple OOS schools an see what they think you should pay to see if you would get need based aid.