Travel

While there are some dangerous areas in Mexico, there are plenty of safe places. Mexico City, is just like any big city in terms of crime. I feel safer there than San Francisco honestly. Merida, Puebla(not super exciting), Oaxaca, Guanajuato (a little sketchy state, but the city is safe/awesome) among others are all safe. The center of town is where you want to be, no need for a car. Just stay away from Michoacan, Guerrero, Jalisco, the Northern border states, don't do drugs or get super drunk and wander around town, and you will be fine.

Getting between larger cities via first class buses is easy. Uber, Metro, buses, etc. My wife grew up in Mexico City and never needed a car, I've traveled solo (male) in almost every state in Mexico without a car for 25+ years. We still go and take our kids for a month every few years.

All that being said, you will be hassled or whistled at, etc as a woman. Macho male syndrome. Dress conservatively and leave jewelry at home. There is crime, don't go out drinking alone at night, and watch for pickpockets in mercados and subways. If you're cool in New York, etc you will be fine in Mexico City, it's a blast. It's intimidating but the food and people are awesome. As a solo traveler you can stay in some hostels which is a good way to meet other travelers to go explore. You could easily spend two to weeks in Mexico City area itself - Taxco, Coyoacn, Chapultpec, Museums, etc

I don't have any advice for Central America other than a relative of my wife lives in Costa Rica and likes it.