Tamil Nadu

Tamil Nadu has many good coaching centers like:
Aakash: The teachers here are good, but it's very expensive if you compare other JEE institutes some of which are better. It's good for medical preparations though.
FIITJEE: They take a test based on which they divide you into batches, the students performing better are given better batches which sometimes demoralizes the students who dint get into good batches. They only concentrate all attention and focus on these students which I personally disapprove of.
Brilliant Tutorials / Career Launcher : Their performance has been depreciating for a while , they provide you basic mentorship and have good test series , though there have been many cases where people have paid the entire coaching amount but not received any coaching or refund.
BYJU'S CLASSES: They have been doing really well in last couple of years as 161 out of 212 students made it through IIT's last year. I have heard they make classrooms a fun interactive session for their students which works in their favor. Also they have been known to return the entire fee amount if the student does not find them good enough for JEE. The only downside is that they accept only a certain number of students and the batches fill up really fast.
Source - https://www.quora.com/What-are-the-best-IIT-JEE-coaching-centers-in-Chennai