You dont have a lot of options for nightlife in this area.
Dont try to leave your hotel's area because this is still a desert and you can fall or find a dangerous animal (leopard , snake).
You can enjoy in your hotel's lobby or sit outside and enjoy the desert silence.
Dress Code: The desert can be very cold place during the night so i think you should take warm clothes with you
Go for a walk in the mountains. Just walk up from hostel Beit Sarah. You will see nice things then. Do be carefull though there aren't fences along the way up and traffic can show up suddenly. Also be carefull not to be bitten by snakes and scorpions while you walk.
Don't expect bars, discos or clubs here. There is nothing but mountains, deserts and the Dead Sea. But something that is nice to do is floating in the Dead Sea at sunset. When it gets dark you can see al the stars while floating. Do watch out though, don't close your eyes, when the wind blows a bit, you'll easily get further then you wish. Also you can easily fall a sleep and you don't want that to happen. The middle of the Dead Sea is very deep! And you can't float across this small Sea, because on the other side lays Jordany and the guards at the borderline aren't the nicest of people.