Down by the Opryland hotel is a KOA, and Two Rivers campground. We've stayed at the KOA several times, very nice. We haven't stayed at Two Rivers, but driven through and it looks good. In between the 2 camgrounds is a large Camping World which may come in handy as their store is very well stocked with Stuff. I assume by "strip" you mean Broadway..where all the honky Tonk bars are etc. To my knowledge there isn't any campgrounds near there anyway. The KOA is a 10-15 minute Uber ride. Also note "Music Row" is not Broadway...two different areas of Nashville. So, even if you could stay near one of the more tourist area's, you still need to Uber to the other area's. The Grand Ole Opry, The Rianan, Music Row, Broadway, the Parthanon, the zoo are all different area's and you'll need transportation.
Also, even if you tow a toad, use Uber. Parking is expensive and you'll pay less with Uber an no worries driving.