Some stylists respect that. Others don't.
Let's say, you walk into a salon in Staten Island and you need a haircut. You will get looooooong layers and a bouncy blowout. They will NEVER give you a chin-length bob. They will NEVER give you bangs. They will give you a Staten Island haircut.
You may also get a stylist at the chair next to you who doesn't mind her fuckin business while you are talking to your stylist. They live in this Staten Island/Jersey Shore Bubble. Your highlights will be chunky and caramel-colored. Staten Islanders say "CARMEL". If you don't want highlights, you will get chocolate brown or black hair.
If you go to Manhattan, you will get what you ask for. Do you want bangs AND a ton of hair chopped off? You got it. Do you want a crazy hair color (purple, red)? Well, your NYC stylist will help you pick one.
There is also an "US AGAINST THEM" attitude amongst Staten Island and NYC stylists. One Lower East Side referred to Staten Island hairstyles as "that Victoria's Secret hairdo". While Tottenville stylists think that "they charge too much in NYC for a shitty haircut".
It is all up to you. It comes down to location and what you are willing to spend. If you want basic, go to Staten Island. If you want edgy, go to NYC.