You can wear whatever you like.
I'd be more concerned about being cautious. The big city has a lot of nice people, but it also a lot of bad people. And some of the bad ones won't think twice about killing you for your money if they think you're a dumb hick who can be taken advantage of. So, if you've got your heart set of taking a look at big city life, please be careful.
In closing, let me share a true story with you. I saw it on cable TV. Can't remember the name of the show, but it was one of they many crime documentary shows that can be seen on cable TV.
It involved a farm family. Mom and the two daughters (in their teens) wanted to visit Florida. Dad decided to stay at the farm and take care of things there while mom and the daughters took an exciting trip. To make a long story short, mom and the daughters never made it back to the farm. When they arrived in Florida, the got lost and asked a man for directions back to their motel. The man gave them directions and offered to take them for a ride on his boat later that evening. They accepted. After he got them out to sea, he raped all three, tied them up, attached cinder blocks to them, and threw them overboard alive. They all drowned. Very sad story. I would really hate to have been the dad. How sad he must have been when he found out what happened to his family.
I'm sure you're wondering whether the criminal ever got caught by the police. Well, yes. It took a long time, but they eventually caught him. I can't remember whether he got life without possibility of parole, or the death penalty. But in my mind he sure deserved the death penalty.
So, I'm not saying that you should cancel your plans, but if you go, it might not be a bad idea to decide to travel with a friend rather than going alone. I realize it's not as dangerous for a man as it is for a woman, but it can still be dangerous. Especially if you're not street smart.
Whatever you decide, be careful, and good luck.