According to your AIR of 59000, and since you have a good budget of 60 Lakhs, the best Institute for you should be Kasturba Gandhi Medical College and Hospital,  Manipal (Manipal University). It is an excellent Medical school with excellent faculty, research and infrastructure facilities. The total fees after 5 years is comes approximate to 35-40 Lakhs. The medical college has produced excellent Alumini like Dr. Devi Shetty of Narayana Health and several other excellent Doctors , Medical Professionals and Entrepreneurs.

Besides KMC, Manipal another good option is Kalinga Institute of Medical Sciences, Bhubaneshwar, which too is a Good Private Medical College and is perhaps near Jharkhand.

As far as State Counselling is concerned, do keep am eye on the State Colleges and the respective State Counselling Dates. You just might have a fair chance into making into one of the following institutes.

MGM Medical College and Hospital, Jamshedpur

RIMS, Ranchi

PMCH, Dhanbad

For more information and college prediction do follow the link below

https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer