Pune is one of the major education centres in Maharashtra and many students come from outside of city or even Maharashtra to get a quality education from Pune. Some of the major coaching classes of Pune that cater to JEE and NEET students are as follows:

Bakliwal Tutorials
M. Prakash Institute
Allen Career Institute
IITian’s Prashikshan Kendra
Prime Academy

Hope I have answered your question. All the best!