Almost all banks provide personal loans which is an unsecured loan as there is no collateral required to be submitted to the lender. With multiple lenders available which includes private and public-sector banks the best bank for a personal loan is one which provides you the best loan offer. 

Your credit health is the prime mover in getting the best loan offers, other factors include salary, working in a good company and proper documents. If you can get a bank or NBFC to give you a personal loan at a low interest rate, low processing fee, tenure you are comfortable with and the loan amount you want as quickly as possible then that is the best bank for you.