I would recommend getting to LAX at least 4hrs before your flight leaves to Nadi....I arrived at 5:30pm LA time and was glad to be there early my flt leaving Tx was cancelled and then the one they rebooked me on was late....so you just never know...I was glad I had allowed plenty of time for that little hiccup.....
getting a day room is the way to go especially after the long flight....we stayed at
Novotel Nadi Fiji Hotel : Fiji Hotels... Novotel it was a nice hotel very close to the airport they had shuttles and are used to accomodating travelers with long layovers....we only used it on the way back since we had made other arrangements on the way over....since we were not boarding The Nai'a for a few more days....there are many hotels in the area that provide the same service
Nadi Airport Hotels in Fiji - DirectRooms
you will arrive Nadi around 5:30am their time....if you want to hang around in the airport you can exchange dollars to fijian money eat or find a quiet spot and wait.... have fun wish I was going back