After you destroy the Institute, the classical radio broadcast signal is destroyed along with it... I loved that radio station a lot since it had some really good classical pieces and its upsetting to me that I don't have access to it anymore... Is is possible for somebody with mod experience to put it back in the game even after the Institute has been blown sky high?

I suggested they make an internet radio mod that had access to various genres of music giving more options than the ones provided by the game.

Likely this sort of thing would require modders to have access to the GECK, since the code to stop that radio station is most likely in a script (or more specifically a quest fragment) that will need to be modified.