OK, you can not get to Bora Bora with AA miles. You can get to Papeete (PPT) with AA miles using TN / Air Tahiti Nui, but then you will have to purchase tickets on Air Tahiti (VT) to continue on to BOB.

However, it has been reported TN is only allowing one J and one F award seat per flight, so flying on awards has been complicated - members have reported acquiring one each ticket and trading a seatmate up to F to allow spouse to fly J, or flying in separate cabins. Coach may be significantly easier, but the words "honeymoon" and "coach" do not work well in the same sentence. (Seriously, it's not a hugely lengthy flight and coach is actually survivable, and 37.5 k miles per person each way JFK-LAX-PPT, iirc.)

There is a decent chance you will have to overnight near Faaa (airport) - we have stayed at the Tahiti Country Club, a fair to middling and not obscenely-priced hotel with pool, etc. on a hill (cooler, views of Moorea and the Sea of the Moon,) near the airport.

Moorea is a short ferry ride away, OTOH, and picturesque - more to do, actually, than Bora Bora, and you can use the jet catamarans from the Papeete main dock to Vaitape - trip time is actually 25 - 30 minutes, depending on the ship, and under $10 per person (aircraft-style seating.) You can range for a hotel pickup, or better, rent a car from Europcar at the ferry landing at Vaitape and self-drive so you can visit sites, eat at interesting restaurants, etc. (Do not waste flying ten minutes on an Air Moorea DHT to Moorea IMO - small aircraft with occasional luggage restrictions and prices significantly higher than the ferry to land on a small postage-stamp strip remote form most lodging, etc.)