Flight
If you're flying, BNA (as IATA and the locals call it) is your only choice! Travel from and to the airport is best handled by a ride-sharing service (e.g., Lyft), which picks up on Level 1 near the ride-sharing signs. Protip: when departing, the security lines for Concourses A & B (United, AA, Delta) are often ridiculously quick (like 5 minutes quick). Even if you're flying Southwest (Concourse C), it may behoove you to use the Concourse A & B TSA line and hoof it over to Concourse C (a short walk, to be sure) if there's a doozy of a line.
House Or Rental
Both our digs and the wedding location are the in lovely neighborhood of East Nashville. There are a goodly number of places available in our area (including at least four or five on our street alone!). If you're looking for a more "downtown" feel, we'd suggest looking at places in Germantown, which is proximate enough to East Nashville but also downtown adjacent and close to the touristy action.
Rental Car
While the header says "Rental Car," our recommendation is to use a ride-sharing service (unless, of course, you're keen to venture nature-y spots outside the city). Being Nashville boosters, Lyft is local and principally what we use (though Uber can be handy at times, and practically all the drivers work for both). But if you'd like to rent a vehicle, your favorite firm will doubtless be represented at the airport.
Rental Car
Again, ignore the header--I just wanted to use the car icon! The "view" is a Google Maps pin of the venue. If you're driving to the wedding itself, the American Legion lot is (thankfully) reasonably-sized and parking is free.