First-time solo female traveler: Which vibrant and safe South American city for 2 weeks in October?

I'm finally taking the plunge and planning my very first solo trip! I have two weeks in October and am dreaming of South America, but feeling overwhelmed by choices. I really want a city that's known for being safe for women traveling alone, has a great buzz, good public transport, and plenty to explore culturally. Any recommendations for where I should focus my research?