“Try not to draw attention to yourself.”
You're from a small town. You're visiting a big city in a foreign country with your fiance, and you're a little intimidated. You're worried about getting robbed or scammed, so you want to try to act like someone who lives in that city. You tell your fiance this.
Try not to draw attention to yourself.
To "draw attention to" something means to do something that will make people notice it. For example, if you are visiting a foreign city and carrying a big camera, a map, and looking around like you're lost, you will definitely "draw attention to yourself".
You can "draw attention to" something with what you say. For example, a political candidate might draw attention to her opponent's weak points by talking about them in a speech. You can also "draw attention to" something with your actions:
I didn't have my driver's license with me, so I tried to drive slowly and carefully so as not to draw attention to myself.
People usually try not to "draw attention" to themselves. When someone does want people to notice them, it's called "getting attention".