I have been to Haikou and meilan airport, so I can tell you something about it.
Unfortunately, there are no trains and buses after midnight.
You can only leave the airport and take a motorcycle or taxi outside.
Or you can take a sleeping bag, spend the night in meilan airport and take the bullet train after dawn.
Haikou and Sanya are big county towns. When you leave meilan airport, you will know when you see various scenic spots.
I hope you have a good trip. If you are satisfied, please accept it.