While I can't really comment on NROTC life as I'm in AROTC, I thought I'd chime in, just in case prospective AROTC'ers happen to stumble upon this thread as well as NROTC live is pretty similar to that of AROTC.
The amount of free time you have really will come down to a few things. How much do you like to party? How good are you at time management? How good of grades do you want? How well do you understand the basics of your classes (for engineering, Calculus, Physics, etc.)? I'm most definitely not an engineering major, however, your first year or so most undergrads take similar courses.
There are days where I have very little to do besides actually attending PT, classes and any study hours. These days you have extra time to hang out with your friends, sleep, or whatever you please. On other days, when procrastination finally catches up to you, you have barely enough time to run to the cafeteria for food between study sessions. I'm currently on the latter schedule. I've decided to stay awake and write 2 papers and study for midterms instead of getting my beauty rest until around 0515 when it will be time run the beautiful hills of northwest Arkansas. 30+ hours later, I don't recommend this route.
Overall, if you are attending the average State U, you will have a good amount of free time some weeks and others you will be busy. It all depends on how well you stay on top of all of your classes.
P.S- In high school, I averaged 7 hours of sleep per night. I now average about 4.5 hours. (Don't be intimidated, this is not all because of ROTC)