Hello, there is no such Institute or class which is the best for NEET coaching but there are some good options for a proper coaching which can help you to crack the test. Some of these classes are as follows:
Conceptree Learning- Adyar for NEET, JEE and Olympiads Coaching,

Appolo Academy,

VVT Coaching Centre NEET and IIT-Jee,

Aakash Educational Services Private Limited.

All d best!