I don't think there is any term like BEST for a offshore bank account. There may be offshore jurisdictions better for your case specific than others. What exactly are your requirements and goals?
Cyprus and Seychelles offer a perfect banking platform and easy to open bank accounts with the major banks in the different countries.
There is a thread on this forum with a list of offshore banks also there is a active user on this forum who suggested a good and trustable Belize bank, search field above this forum may be your friend