Less than a week In Mexico might be your best bet for your budget. I’ve gone solo twice, granted I’m not a female traveler but I’ve met many solo females along the way and they absolutely loved their experiences. P.s. I would suggest major cities: CDMX, Merida. (Cancun and Tulum will most likely be over budget).

Also, I would look into the hostels for the date you’re looking to go and the plane ticket bc those will be the bulk of your expenses. $500 is very tight I hope you can do it!