That’s actually possible with the current tools in theory, but sadly it’d require a bit of work. I’m away from my computer as I’m writing this, so this is a basic idea of what you’d need to do.
Basically, Apu’s level (Level 5) has a .RMS script (which controls what music plays in a level essentially) that has several short audio files tied to him driving around while in a car. This makes Level 5 unique as it’s the only Level in the game that has multiple tracks associated with driving around in a car while not on a mission, and they’re randomized.
Using Tools some of Lucas’ Tools, you can take a track you’d like, downsample it, and convert it into an audio format the game supports. You can then use RCF Explorer to grab the RMS file for Level 5, edit it to replace the multiple tracks associated with driving around in that Level, and insert your own tracks. You could then use Lucas’ RMS Builder to obtain a fresh RMS script, and throw it into the Level of your choice.
One of our users (Thomas/hipporeno)
did something like this a little while back before RMS script editing was a good thing (which didn’t allow for custom track length), and got results very similar to that of one of the radio stations present in a GTA title. It’s where I got this idea from.
Sadly it requires a bit of work, but is very much do-able currently if you have the time! Alternatively, you can mute the in-game music through the Options menu and play music in your favorite audio player.