As you say, places near academic institutions should be pretty good for you. Oxford or Cambridge in England may not be too expensive. Edinburgh or Glasgow would be cheaper even.
In any case you may consider enrolling in some kind of academic research program. Pursuing your own intellectual thing by yourself will be incredibly tough and lonely.
If you aren't part of the university then Oxford and Cambridge aren't great. I think the pressures from tourism force them to isolate themselves. They are expensive as well.
"Pursuing your own intellectual thing by yourself will be incredibly tough and lonely."
Oxford and Cambridge themselves are exorbitant, though if you like small-town life and are happy to get the bus/train into the city, there are some reasonable options nearby (I live in a tiny town 15 minutes from Oxford on the train, for example).
In any case you may consider enrolling in some kind of academic research program. Pursuing your own intellectual thing by yourself will be incredibly tough and lonely.