Independent research? Though I agree, if you have to do it within an institution, something like academia is probably best, or maybe a blue sky research facility, if those still exist.
Graduate school has a number of extremely important advantages over independent research, at least when you're getting started:
1. Mentorship.
2. Easy access to the rest of the research community.
3. Access to resources: libraries, journal subscriptions, and, most importantly, funding.
