Would this be an o.k. sentence to use in my essay?

This would still be the closest I had ever been to someone with their name used in the same sentence as the word “famous.”

Or should I just say, "This would still be the closest I had ever been to someone famous" The reason is, is because the person wasn't exactly world-wide famous but she was well-known in the city itself. Is that still considered famous?

Yes, that's considered famous, although 'very well known' works, too.

I'm wondering about your use of 'would' though. Are you writing about a possibility? Or a reality?