I suppose that's more or less important whether you're running in a busy city or out in the countryside though.
Either way, recent high end smart/sport watches usually have some sort of music playback support for folks who want to exercise with music but don't want to lug around a phone.
You may not hear mountain lion, but you may hear stray dog.
I have a Garmin smart watch that supports audio playback but it's a hassle to use because I have to load or sync recordings in advance. Streaming audio on my phone is much more convenient. Plus I have my phone with me anyway in case I want to take a picture due Strava or something.
I will personally attest to the Sansa clip + $10 earbuds being the best workout audio combo available.