For me, Calculus isn't a bad place to start. Its assisted me in calculating divergent series, proving binomial expansion, calculating some harder summations, providing bounds, and simply giving intuitive sight into how a function may work.
Calculus isn't too hard, and you don't really need pre-calculus to learn it. Calculus is just a little different from previous math courses in the topics. Its like the jump from middle school math to Algebra, just a little harder and makes you think differently.
Another nice topic of interest to you might be modular arithmetic. It is rather easy, and when you learn things like Fermat's little theorem and basic manipulations, you can do cool things like determine what the last digit of $47^{2958}$ is. (It also helps you make faster choices on multiple-choice questions involving whole numbers. And if you have a younger sibling in elementary, teaching them the basics to modular arithmetic could help them in math... wish I knew ALL of modular arithmetic in elementary. When you learn modular arithmetic, I bet some of the material will be so easily you'll say "I've done that before!")
Summations are also fun. When you learn calculus, summations become easier to deal with as well (for me at least). Also, making formulas with summations gets you into thinking about how you can provide proofs sometimes, and other things like that.
Set theory is a short(ish) topic that is really interesting for most people. It is basically the theory of infinity, and a nice video that captures the gist of set theory is Vsauce's "How to count past infinity?" video.
Number theory might be a bit harder, but you could potentially learn some of it.
And don't expect all of this to come easily (maybe the modular arithmetic), so take your time, and if you get stuck, we'll be right here to help you.
Ranked in easiness according to my opinion (difficulty based off how hard to get started in the material):
Modular arithmetic (easiest)
Calculus and summations
Set Theory
Number Theory
Also, I have to ask, do you intend on math courses for credit, or math subjects you want to learn on your own with no other reason than that your just nerdy like that? It makes a difference.