Yes the metro parks will be open for sure.
Centennial Park is fairly large, but parking will be limited.

August is very hot and humid even on a good day so consider bringing a back pack or cooler with plenty of water, a battery operated fan of some sort, a folding chair or blanket to sit down on and pack a picnic lunch of some sort as food options will be fairly limited in and around the parks. Bathrooms are not easy to find and may not be in great condition either.

Of course don't forget your viewing glasses.

I can try to contact my employer tomorrow to see if they will permit the public to enter the campus viewing area or not as I hope to bring some of my family with me.
The Opry Mills outlet mall and Gaylord Opryland have huge open parking areas adjacent to each other and lots of places to eat plus find a toilet as well as to take a break from the heat but I would arrive super early if that is your plan as traffic will be very heavy-it is also fairly close to BNA.

Parking is usually free at the mall but not at the resort.

I had not thought about the zoo(it's not a very good zoo in my opinion) and there may be a lot of kids and home schoolers going there as well as at the Adventure Science Center and Planetarium-I would avoid that location like the plague even though there is a great view of downtown Nashville from that area.