Making LEDs dance around with music is a fun project, and a spectrum visualizer is a great way to do that. Where you start on one of these projects is of course a huge question, but why not check out jolliFactory’s Spectrum Visualizer PCB board.
This is a carrier board for two MSGEQ7 chips which process an audio input into different outputs based on frequency. Add these chips and an Arduino Nano to the board and you’re in business. The kit includes all the resistors, capacitors, and audio jacks that are needed.
See its capabilities demonstrated in the video below in a 3D visualizer made with JF’s LED Matrix Modules. You can also use it with more normal-ish LED assemblies in a 2D matrix like this 16×16 LED version.
For another take on audio experimentation, check out the Audio Hacker shield to experiment with sound using an Arduino. Perhaps you could use both at the same time for an interactive AV experience!