Virtually just outside the store are a pair of kids who say:
"Hey, hey, didja know? Didja know? You can, like, BECOME stylish! Wow!" "Yup! You can have your Furfrou's long hair cut in all kinds of ways!"
I had 5 badges and had visited just about everything in the city, and couldn't get in. I styled my Furfrou, and then they let me in.
I wouldn't be surprised if that was actually the only requirement - it's a pretty obvious hint in retrospect. --- Have an irrational need to go and play an awesome free online CCG? Play Cardmaster Conflict! http://www.cardmasterconflict.com/cmc/