Yes, the sentence is a bit long and wordy though. If you wanted to keep it together, you could do something like:
Charging entrance fees for public places such as national museums or art galleries, where people can explore their own history and heritage, leads to detrimental social issues.
Or even:
Charging entrance fees for public places such as national museums or art galleries – where people can explore their own history and heritage – leads to detrimental social issues.