It will be easy to get there if you are familiar with coming into Nashville already. And at that time of day, you definitely shouldn't have to worry about traffic! They are doing a lot of construction on parking & routes in/out of the airport (there's no way they'll have it done by then), and there are a lot of options for parking. You can check the website to find where you want to park/how much each lot costs per day. Check-in there is easy, too. You can go through security near the SW check-in, and then just turn left and head to your gate, which will probably be one of the last ones.
But if you're a Starbucks girl, be aware there's only one and the line's always long.
There are other options for coffee/breakfast at that time of the day, though. DH has become partial to a cafe right as you go down the ramp, on the right. They're good, but super slow every time we're there. If we're flying out early, I always make him build in enough time to get something to eat before we get on the plane. I'm not ready to eat before we leave home, but by then, I'm starving. And there aren't really any options to hit before you arrive at the airport.