Spending the night at the airport
Tel Aviv airport is a big and busy place, so it is difficult to find resting spots, and there is also a lot of noise and bright lights. Get some earplugs and a sleeping mask, and have your ticket ready, as the security staff may ask to see it to let you stay inside the enclosure.
Where to rest:
Most seats in the airport have armrests, but you can find some comfortable couches in the Departures area, next to the food court. There are a couple of VIP lounges inside Terminal 3, one of which is open 24 hours a day, although the maximum stay is 2 hours. SEE VIP LOUNGES
As for hotels, the closest are found in the city centre.
Baggage: The left luggage service is not available during the night. This means you will have to keep your bags with you until checking-in.
Eating and drinking: There are several options throughout the terminals, but none of them are open during the night, except for some vending machines.
Wi-Fi: Free and unlimited.
Other services available around the clock: ATMs, currency exchange bureaus, synagogues, baby changing room.
The closest accommodations are found inside the city. Avia Hotel (Tel +972 3910 9104), Kfar Maccabiah Hotel & Suites (Tel +972 3671 5715), Sadot Hotel (Tel +972 8919 9100), Star Guest House (Tel +972 502 526 278), Apropo Hotel (Tel +972 3535 2724), Nahalat Yehuda Residence (Tel +972 547 557 793), Hotel La Guardia (Tel +972 775 324 813), Overstay Hostel Tel Aviv (Tel +972 534 210 200), Ruth Daniel Residence Hotel (Tel +972 3526 4526), Florentin House Hostel (Tel +972 3616 4449).