First of all, unless you get there VERY, VERY early, you'll likely be forced to stand in the street, not in the actual "park".
I tried the whole Riverfront Park thing several years ago, and I'll never do it again. Parking is a disaster, and it can take hours to get back to the Interstate. Not to mention the fact that there are so many people crammed into a small area, you will end up being covered in the sweaty DNA of anyone within 100 feet of you. It was not very pleasant for us.
We now park in a lot on Shelby St, right across from the Exxon and LP Field. Easy to get in and easy to get out. Great view, and plenty of room. We generally get there a little early so we can fire up the grill. Bring your lawnchairs and a cooler.
If you are worried about the musical aspect of the show, don't. You can hear it pretty well from the lot, and many folks tune their radios to whatever station is broadcasting. You won't miss a thing. It's the best place we've found to watch Nashville's Fireworks show.
FYI: If I recall correctly, it costs $10 to park in the lot. Could be more, or could be less. I can't remember.