How much will it cost to go to each school?
My gut tells me that in CS what you can do on the job will overtake the name of your school pretty quickly. But I’ll let others on this forum comment on that further.
If you save money going to U of R then you can use the extra funds to get started in NYC later. A school like U of R will have recruiting opportunities in general, but you would need to ask Career Services about their CS recruiting. Maybe ask for a list of on-campus recruiters and recruiting events. That may give you an indication. Also ask them about their alumni connections to CS in NYC. Networking through alumni is a way to get jobs.
If your main concern about going to NYC is to find inexpensive CS training and then network from there into a great job in NYC, then you may want to consider CUNY schools. There are several. CUNY offers rock-bottom prices for education in the City and virtually identical networking opportunities as more expensive institutions. CUNY is a system of schools within NYC. The CUNY system has several schools offering different CS opportunities.
You can follow the link below to search for CS degree programs. Search for “computer science” and it will generate a list of CUNY schools that offer CS. Each school of CUNY has its own feel, from Hogwarts-like on its own campus to very modern and NYU like, set in the middle of Manhattan. You may want to see if any of these schools appeal to you – http://www2.cuny.edu/admissions/undergraduate/explore/programs/
Also be aware of the Macaulay Honors Program, which attracts Ivy-level students. The deadline for applying is quite early as it seems to want to skim off those students before they get accepted elsewhere. Macaulay offers free tuition plus a stipend. http://www.macaulay.cuny.edu/