As one of my friends is in the Computer Engineering Department of NIT Surat. I might be able to answer the question.
NIT Surat is well known for its Mechanical Branch. Compared to all branches, the quality of professors in the Mechanical Department is far better than the other branches.
If you have any interest in robotics we have Drishti, a student club that is completely dedicated to robotics and SAE for designing cars.
Thus, it is suggested that if you want to pursue mechanical engineering then go for NIT Surat. Whichever institute you choose you won't regret much. NIT Calicut also has good reviews on the internet.