I suggest taking a more discrete course such as number theory, or try competitions such as AMC/AIME/USAMO. These will definitely help you be more "well-rounded" in terms of math ability, as you'll be able to do proofs and be creative with finding the solution to a problem (e.g. proving an inequality using an entirely geometric method, which students almost never see in a standard HS textbook). Also, qualifying for AIME/USAMO is a big plus on any college application.
You don't necessarily need to rush through all the calculus, group theory, real/complex analysis, or algebraic geometry courses. Calc BC is definitely a good course, but don't complete the standard calculus curriculum without knowing how to do proofs, for example.
This article basically sums it up: The Calculus Trap
AoPS also has some good online courses.