For the majority of people Algebra.. Highest recommended, diff eq, linear-alg.. That's prettttty much everything you'll need to know in life that's readily applicable..
Solving differential equations is fun enough, but I agree with you that algebra is a better skill. In particular, everyone should learn to bust out nice proofs and show off their commutative diagram drawing skills.
I recommend the Snake Lemma, because it has a cool name, takes a nifty/elegant proof, involves really nice commutative diagrams, is pretty useful in graduate level mathematics, and because its proof showed up in the 1980 film
It’s My Turn, perhaps the only time some real mathematics showed up in a Hollywood picture.
I mean, check this out:

(taping a snake to the diagram is optional)
For those not into algebra, differential geometry proofs are an okay alternative. Riemannian manifolds are cool.