If a school offers merit aid (like Case Western, Santa Clara, Pitt, UMass, etc), then don’t just look at the sticker price. If you are showing real demonstrated interest to them and they think they’d have a legitimate shot of landing you if they gave you enough merit aid, then they will try to entice you with it. So the sticker price may not be the price that they would actually end up asking you to pay.
Did you take the PSAT this year? If so, is there a possibility you might become a National Merit Finalist? That could open up a lot of options that would be very financially attractive. A current estimate for the cutoff score is 220, though the range of 218-221 is where the cutoff is likely to be (source).
For instance, New Jersey Institute of Technology would give you free tuition & fees and you’d be eligible for potentially more honors scholarships, up to full room & board (source).
I’d recommend applying to U. of Illinois - Urbana Champaign which would be a reach, but it’s arguably one of the top CS schools in the country, and the cost would be way less than most of your privates. I’d also consider U. of Maryland.
Since a lot of your reach schools are on the small to medium size, I’d also take a look Rensselaer Polytechnic, U. of Rochester, Rochester Institute of Technology, Rose-Hulman, and Clarkson.
ETA: Adding on Stevens Institute of Technology which offers scholarships of up to full tuition. Stevens & NJIT are both quite near NYC (Stevens is literally across the river). Also tagging @DadOfJerseyGirl for his insight.