I'm a 17 yr old australian girl and I want to do a solo overseas trip. How to stay safe?

I really want to go to Mexico but everyone keeps teling me how 'dangerous' it is. Pfft. I was also going to travel around the USA for about a month. Any suggestions on staying safe/fun things to do in the USA? I'm really looking for an adventure so stuff thats 'off the beaten track' would be awesome