My JEE Advanced rank is 13K and I will get an approximate 20K rank in the JEE Mains. Should I join CS in Nirma University or do I have better options?

You have a lot of better options than Nirma University. My brother is an alumnus of Nirma University and according to his experience, the CS department is good but you can easily get into DAIICT or some of the top NITs with your rank.

You can perform an analysis and decide which NIT is more suitable for Computer Science Engineering. Choose the one which is the most suitable one for your career goals.My advice for you would be to choose your college wisely as you have a pretty good rank. Do not opt for any of the IITs just because of its brand name.

Even if the Computer Science department of an IIT is not so good, you should instead go for a well-reputed NIT. At the end of the day, what matters is the quality of knowledge you obtain and not the name tag of the college you get enrolled in.