Julia Robinson! I recommend her for a high school audience for a few reasons:
Mathematical reasons: She is best known for her work towards the solution of Hilbert's 10th Problem, regarding an algorithm for solving Diophantine Equations. High school students can absolutely recognize and solve particular Diophantine Equations. Furthermore, and more relevant to Robinson's work, I believe high school students can appreciate (upon seeing examples) the subtle dependence of such equations on their coefficients.
For instance, ask a high school algebra student to experiment and find all the solutions to, say, $6x+15y=33$. Then, ask them to solve $6x+15y=34$. What changes? Give them some random coefficients for $ax+by=c$. What would they do? Can they generalize to more variables?
Then, work with them on a quadratic equation, something like $x^2+1=y^2$. Can they find any solutions? What about $3x^2-5y^2=2$? Do they see how hard it is to get a general method?
Then, you can start to talk about what Hilbert's 10th Problem says. This can facilitate several interesting discussions for a high school audience
- Solving equations in integers (Why have mathematicians been interested in solving them since pretty much antiquity? Where do they appear in real life?)
- Algorithms and decision procedures (What is an algorithm? What makes one better than another? Do we care about how efficiently they can run, or how easy they are to describe/implement?)
- Logic and philosophy of mathematics (What does it mean to prove something? What does it mean to disprove something? What does it mean to prove that there is no procedure that could solve every Diophantine equation?)
(I understand this doesn't really address the full depth of Hilbert's 10th, but if you're looking to pique the interest of a high school audience, I believe this should suffice.)
Historical reasons: Julia Robinson is one of the more notable and renowned mathematicians (no need for "female") of the 20th century, especially in America. Despite this, she had difficulty securing an academic position. But despite that, she went on to obtain such a position and became the first female president of the AMS. Along the way, she devoted much of her time to other interests, including political campaigns.
Surely, she can spark many interesting discussions for a high school audience!