Should I leave NITK Surathkal CS for IIT Gandhinagar CS? I've finished my 1st year from NITK.

You should go to IIT Gandhinagar. That being said, if you have obtained the CSE degree course at Gandhinagar, then the most probable rank you ought to have is under 1800, since the closing rank is around 1800–1900. In that case, you can opt to go for other old IITs’ by compromising with the branch. You will get far better students at old IITs, which can be a plus side to your personal development and further enhancement.

For the most part, the problem with the new IITs is that they lack to provide a greater established alumni network and good infrastructure. However, since IIT Gandhinagar was established back in 2008, you can expect decent infrastructure and facilities.