Unlike a savings account which is opened by, for and at a bank, PPF is not a bank product. PPF comes directly under the Department of Economic Affairs and banks have to just facilitate the opening of accounts. Hence, banks cannot force you to open a savings account in order to open a PPF account. However, if you open both in a particular bank branch it would be beneficial in terms of facilitating transfer of funds, monitoring etc.
You can open a PPF account at a host of bank branches and of course the post office. Some of the bank branches that offer the services include State Bank of India, ICICI Bank, Indian Overseas Bank, IDBI Bank, Punjab national Bank, Vijaya Bank etc. Take a look at the detailed list here
PPF is the only product in the country which offers you dual tax benefit under SEC 80C, as well as the interest income being tax free in the hands of the investor.