A great reason to apply to private colleges in general for CS would be that you might find a few at which class sizes are limited to about two dozen students, which would create a dramatically different experience for you compared to what you might encounter at most public universities (as well as at many large private universities). From your listed group of private colleges, Princeton might offer you the greatest contrast in classroom experience to that of UCD, and could be worth its cost premium on this as well as other bases.