Can anybody please tell me what is the range of Unicode printable characters? [e.g. Ascii printable character range is \\u0020 - \\u007f]
First, you should remove the word 'UTF8' in your question, it's not pertinent (UTF8 is just one of the encodings of Unicode, it's something orthogonal to your question).
Second: the meaning of "printable/non printable" is less clear in Unicode. Perhaps you mean a "graphical character" ; and one can even dispute if a space is printable/graphical. The non-graphical characters would consist, basically, of control characters: the range 0x00-0x0f plus some others that are scattered.
Anyway, the vast majority of Unicode characters (more than 200.000) are "graphical". But this certainly does not imply that they are printable in your environment.
It seems to me a bad idea, if you intend to generate a "random printable" unicode string, to try to include all "printable" characters.