I agree with coolmon42 that the weather in late April should be good, warm but not too warm. The campground info posted above is right on. I'll add one more, Countryside RV Park just off I-40 between Mt Juliet and Nashville.
Start with the Nash Trash Tour as it's a hilarious way to see downtown Nashville. Catch a show at the old Rhyman Auditorium or at least take a tour of this original home of the Grand Ole Opry. Check out the shops, restaurants, and honky tonks just a stones throw away on "lower Broad" AKA Broadway. Visit the Country Music Hall of Fame and the historic Hatch Show Prints another block over. The Frist Art museum is on Broadway and next door is the Union Station Hotel, a historic train station that has exquisite architecture in the common areas. The Loveless Café is on the western edge of town but has excellent country vittles (food) and a wall full of photos of famous people that have dined their. On Wednesday evenings you can attend a live radio show in their Loveless Barn out behind the café. If they'd like to see some of the countryside they can take a quiet drive along the Natchez Trace that starts just west of the Loveless just watch out for the many bicyclists. This is just a sampling, there's much much more to see and do in Nashville.