I attended CCNY over 25 years ago, so my information might be a bit dated, but their Engineering School is well respected throughout the Tri-State Area. There is also a very large alumni network in that area. I did my undergraduate degree at their Engineering School and graduated in four years (no summers…had to work). I was recruited by one of, if not the top, R & D Company at the time and that company sent me and many others new graduates off to do their graduate degree with their One-Year-On-Campus Program (all-expense paid+stipend). I applied three to only the top five graduate schools for my Engineering field (the Company picked the five schools). I was accepted into 2 out of the 3 programs (University of California - Berkeley and University of Michigan). I finish the program in 10 months, with pretty much all As and return to the company to continue employment. Believe it or not, I have had Company Representatives approach me to seek employment with their company, based soly on the recommendation from some of my Professors. When you have excellent grades, they will seek you out, as oppose to the other way around. I had multiple job offers when I graduated from CCNY, but chose the R&D organization because of the chance to attend Grad School free of cost, plus, it was just a great company to work for at the time.
While at CCNY, I got a Research Scholarship with one of my Professors in my senior year and worked at one of the local Utility Company in the Summer between my Junior and Senior year. The biggest challenge during my first year at CCNY (apart from having very little money) was getting into certain courses, especially during my Freshman Year. If you get priority registration (a plus for Macaulay Honors), your life at CCNY will be a lot easier and allow you to complete your degree quickly. Back when I attend, the competition for Chemistry I & 2, Physicas I & II, Modern Physics, Computer Science and a large number of the General Education Classes were fierce. We did not have computerize registration in those days, so it was PITA to navigate the registration process. Apart from registration, I did not experience any type of bureaucracy at CCNY. Financial Aid Office can be a bit tough, due to the shear number of students that attempt to access that office at peak periods (start of the semester).
The Engineering School was probably over 80% Foreign Students (people born outside the US), which prepared me well for my interactions with Graduate School Students, which was close to 100% International Students. If you are not comfortable in an environment with a high number of Foreign students, don’t go to CCNY! The location of the School can be a turn off for many, but the fairly new Grove Engineering building is a plus. They have since added a few new programs to the Engineering School since I attended (e.g, Computer Engineering, etc.). Also, given the cost of CCNY, compare to the other Schools on your list, CCNY is a bargain by many factors of magnitude! I was able to graduate with little or no debt, since I was very adept at scrounging for scholarships and grants as an independent student.
If you did any type of AP Calculus Courses in High School, CCNY had (I don’t know if it is still available) an Accelerated Calculus series, where you did Calculus 7 & 8, instead of the typical Calculus I, II and III. This option was determined by your Math Score on their Entrance Exam and this allows you to complete your Degree in four years (back then we were required to complete 136 credits to graduate with an Engineering Degree).
The point of my long post is to demonstrate that getting an Engineering Degree from CCNY will allow you to get into any of the top Graduate Engineering programs in the Country, give you access to Internships and Research opportunities. It is totally up to you and the grades you achieved while at the school. Some of my peers that graduated the CCNY Engineering School with me and was employed by the same R & D Company, went on to Georgia Tech, Columbia, Stanford, Berkeley and a few other Top Engineering Schools.
I think Columbia and Cooper Union a great Engineering Schools if you can afford to attend. In IMHO, Cooper Union is just too small a school, with limited social interaction with students across multiple disciplines. Frankly, if you intend to go on to one of the top Graduate Engineering School, any of the schools listed, will suffice. The key here is getting exceptional grades, which will open many doors going forward.
BTW, I made an attempt to transfer to Columbia University during my Freshman Year, but was talked out of it my one of the Professors that I sought a recommendation from. It was his opinion that I can get an excellent Engineering Education at CCNY and that the Engineering School well respected. I couldn’t afford Columbia any way, but would have gone there if I could (I loved their campus). 