Regardless of where you research (unless independently), you will end up doing research sanctioned by your employer. You would need to convince whomever is sponsoring your research, or who you are doing the research for, that your research is value added.
If you are under a mentor, you need to realize your position as the subversive. If your mentor agrees you can pursue your research under thier guidance, then that is ok. Insubordination is frowned upon.
In looking for a mentor, start with large corporations, such as 3M, which does have a mentorship program.