You might try the State Parks to see if any are open and can give you a better rate, but $200 a week for hookups/facilities is pretty cheap. Might also be a city/county/community park that is still open, which tourist information in Nashville could help you with.
If $ is a serious issue, and/or you want to be really close to those grandbabies, might consider your daughter's driveway or in front of her house. An extension cord will keep your electric running, you can help with the electric bill and can probably find a truck stop to dump when you need it.
Good luck and have a great trip.