Can you track an iphone to see what city it's in?

I'm 19 and going on vacation soon, but my parents can't find out about it. Don't try to tell me not to go, I'm not going to listen, I already have my mind made up. However my parents are in charge of my cell phone. I'm paying for my own flight etc on my own debit card, but is there anyway the cell phone bill will show what city I'm in? I'm going out of state so they will know. I have an iPhone 4S (AT&T). I've researched and I don't think it does show up, but just in case, I want to double check. Thanks.

Added (1). Yes but will it show up on the phone bill?

Yes, you can download an app called "find my iPhone" and it works really well

Find my iPhone can show you the exact address of your phone, but they're old and probably don't know how to do that stuff. My main concern would be tracking your debit/credit card transactions.

Just go under the icloud settings in preferences and disable the "Find My Phone" setting.

@Additional - The only thing the bill shows if they opt for the full disclosure bill (something that most people do not) is time, duration and number called. I've never seen location in any of my phone bille either online or dead tree copy.

A: Hi Ques
Iphones have gps device in it. Just by setting up the Find My Iphone app on another iOS device will show a list of active devices. Among those devices you can verify for it's location. When the GPS location is locked upon then Find My Iphone will show the exact location of that device that you've been looking for.
Your location will not be reflected on the billing unless, your parents would opt to let your current location be posted on the billing.