As someone who grew up and did their undergraduate degree in the same small hometown, I was so glad to have done my postgrad in London.
Whilst London is expensive, there was so much more pros that came with being there: experience of living in a city, studying at a top university, meeting diverse/multicultural/like-minded people, the opportunity to see and do so many things, career opportunities, personal and professional growth etc
Being in London (even though it was only for a year) offered me so much more than my hometown could ever do. And surprisingly, I really thrived on the busyness.