Running

Some events do specifically ban music so have a look at the race information, after that ts up to you.

I would advise not running at all for roughly a week to keep you fresh, doing light exercise and as much stretching as you can to keep you loose and flexible.

Some core stability stuff can't hurt...

erm, it can. especially if it'd be the first time doing core stability stuff - I.e. targeting muscle groups not conditioned to being targeted. DOMS anywhere on race day would be a shitty way to start the race.