Bakliwal Tutorials is the best institute for IIT in Pune for sure. Before I give my reasons, the results speak for themselves. Other institutes show their results from their branches all over India, but when you look at results in Pune, you will understand BT is at whole different level. Their Pune-only results compete with big institutes spread throughout the country.
Why I think BT is THE best in Pune is because the teachers not only know what they are teaching, but also know HOW to teach. The teachers know exactly what your strengths and weaknesses are and guide you throughout however many years you choose to be with BT.
Another unique thing about BT is that they focus more on making your thinking ability more powerful, rather than just giving you all the information. Logic as a subject is taught in foundation courses. Whizzkid is an exam held by BT every year which tests only your Logic.(Whizzkid is NOT an IQ test. They do not release the papers but if you want to know the level of the exam, you can look up Technothlon organised by IIT Guwahati where the level of the questions is the same as Whizzkid)
The students at BT are excellent, academically and socially. Even after passing out from BT, they are always ready to provide guidance to their juniors during their years of preparation for IIT's and also for choosing which college to take.
Can't thank BT more for the 4 years I have spent here.