This is a matter of personal taste in my mind. I may like some type of music and not another that you like and you may not like my favorites. So it seems important to put some context to this question and see if any answers may come up.
While driving to the eclipse.
Obviously this music is your own to hear, and those in the vehicle with you. So crank it up and have a good drive! Pick those songs you love to hear when driving. Just be careful, there are other eclipse chasers on the road with their music on too.
You probably know what music you'd like for this part. Or it may even be a recorded book reading. So I see no reason to comment further.
Before the eclipse.
Wear headphones. Your music may not appeal to all around you. This is just a courtesy thing. Again, pick the music you love, that gets you up, that gives you a smile. Just don't sing out loud and dance too much.
I cannot recommend any music for totality. It has music of its own. The crowd cheers as the diamond ring starts totality, then subsides, the camera click away, comments about this and that are made, then the crowd noise increases as third contact approaches climaxing in another glorious diamond ring. You don't need additional music in the background, just take it in with all your senses.
If others near you enjoy your type of music, turn it up (otherwise be polite). It is party time to celebrate seeing the eclipse. You are now an eclipse chaser. Your musical tastes may not change but your appreciation of the universe will.
So what music do I like? I like something calming before the eclipse. Mozart, Holst, Cronixx, Marley, Pink Floyd, Grateful Dead, and so forth. After the eclipse, almost anything goes!