HDFC, ICICI, and SBI Bank allow the opening of PPF accounts online. The current PPF interest rate is 7.1% which is the same for all the banks. Minimum Rs. 500 you need to deposit and it will go upto Rs.1.5 lakh annually.
Look for a bank known for good online service. Do some research online or visit banks' websites to compare features and choose the one that best suits your needs.