To get more style in X/Y, you can do the following things in Lumiose City:
Ride a Gogoat (+1)
Use a cab (+1)
Finish the first five Looker chapters (+5)
Finish the final Looker chapter (+20)
Get a haircut/change the color of your hair (+2)
Create a PR Video (+1) (To get style from this, you have to use the "Create by yourself" option and not "Surprise me".)
Buy a meal at Restaurant Le Nah (+2)
Test a team at the Battle Institute (+1)
Buy a Lumiose Galette (+1)
Completing a perfect job at Hotel Richissime (+3)
Enter the Lumiose Museum without buying the audio guide (+1) (No style is gained after the audio guide becomes free once you get 90 style.)
Enter the Lumiose Museum and buy the audio guide (+2) (No style is gained after the audio guide becomes free once you get 90 style.)
Take the train at Lumiose Station (+1) (Only works when you're going from Lumiose to Kiloude
Create a Berry Juice at the Juice Shoppe (+2) (Can be given the woman or a Pokemon.)
Buy a Berry Juice at the Juice Shoppe (+2)
Buy something at the Poké Ball Boutique (+2) (Style is gained every time money is given, so that means you'll get more style from buying three things separately than three things together.)
Buy a meal at Restaurant Le Yeah (+3)
Win a prize at the Loto ID Center (+1)
Buy a meal at Restaurant Le Wow (+4)
Buy a meal at Sushi High Roller (+5)
Buy something at Boutique Couture (+3)
Have a Furfrou styled at Friseur Furfrou (+2)
Buy something at Herboriste (+1) (Similarly to the Poké Ball Boutique, style is added every time money is given.)
Buy a Fire Stone, Leaf Stone, or Water Stone at the Stone Emporium (+2) (Similarly to the Poké Ball Boutique, style is added every time money is given.)
Also, if the lady that isn't letting you shop you're referring is the lady in Boutique Couture, you'll need 25 style in order to be able to shop. To get deeper inside of the Lost Hotel, you don't need style. Instead, you need to know the first four roller skating tricks.
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