So one thing to consider is most public universities have little or no need-based aid for out of state students.
Private colleges and universities might, however, give you a lot more need aid, or possibly need+merit.
One general issue in college admissions is that when some people think about private institutions, they only think about the most selective private institutions. However, there are many excellent private institutions that are selective, but not among the most selective.
For someone with a CS interest, there are a variety of private colleges you could consider. One way to generate leads would be to look at this list of top feeders to CS PhD programs, including the per capita version. Not that you have to want to get a PhD, but if a college does a good job supporting students who want CS PhDs, that is indicative of a good CS department:
With a CS interest, I think you might want to check out colleges like Olin, Rose-Hulman, RPI, and WPI. Try running their Net Price Calculators and see what they say.
I think DePauw, Trinity University (Texas), and St Olaf could be interesting options as well. And more, I am just picking out some ones I think might be particularly suitable for you to consider.
All these schools are selective in their own ways, but I think one or more of them might well go for your sort of profile. And applying to a mix of colleges like that could give you alternatives to consider that would actually be competitive on cost with your in-state options.