There isn't much to do nearby the airport, in terms of tourist attractions, and given your short time frame, I would probably stay put. Rushing to the Acropolis is just not worth it, as the lines are long to enter and you could spend days there just soaking in all the history and walking around.
According to this article, there are 8 things to do on a layover at Athens Airport:
- Eat
No matter what time you arrive, you can grab a bite to eat, as several restaurants are open 24-hours. Stop at one of the Greek options, including the Kir-Yanni Wine Bar, or head to any of the several European cafes and sit-down restaurants. Of course, you’re never far from a McDonald’s or Starbucks either. A grocery store is located pre-Security, so venture there if you need to pick up any snacks for the next leg of your journey.
- Hang out in a lounge
Airport lounges are no longer for fancy flyers only! No matter what class you’re flying, you can
head to an airport lounge and enjoy good food and drinks, hop on WiFi, and catch up on the news all in a quieter environment than the main terminal. There are several lounges that welcome any travellers regardless of airline or class of service – simply buy a pass online or use your membership in a lounge program to gain entry. See our Athens Airport Guide for locations and amenities.
- Get a dose of history
For many travellers, Greece is synonymous with history. Even if you’re only in the country for a layover, you
can still take in some ancient and more recent past. The Main Terminal features permanent exhibitions from the Acropolis Museum in town. There’s also the Exhibition of Archaeological Findings and the Eleftherios Venizelos Permanent Exhibition is dedicated to Greek aviation history. Open daily from 6am – 11pm.
- Go exploring
Beyond the airport Layover SightseeingIf you’ve got a few hours, you can take advantage of the airport’s location to get
out and about for some fresh air and local culture.
Layover under 5 hours The airport’s location means you’re within easy range of a couple attractions, and sometimes you need to just get out and breathe fresh air, even if it’s only for a couple hours. Tour a vineyard and sample the wines at nearby wineries like Gikas Winery, Domaine Papagiannakos, and Eklektikon – they may even provide airport pick-up. If you’ve got the kids in tow, take a 10-minute taxi ride to the Attica Park Zoo. If you’d rather shop, international superstore IKEA is located a few minutes away by bus or taxi, or pop over to the McArthurGlen Designer Outlets, a quick 15-minute taxi ride.
Layovers longer than 5 hours The Athens metro system can have you in the heart of Athens in about 45-60 minutes, so you’ll want a few hours to head into the city. Take a traditional walking tour by getting off at the Acropolis metro station; stroll along Dionysiou Areopagitou Street, a pedestrian road that leads to the Acropolis and accompanying museum. Or pop off the metro at the Monastiraki stop, and wind your way through traditional neighborhoods with white homes, cafes, and low-key Greek restaurants.
- Shop
A layover is often the perfect opportunity to shop at your leisure, and this airport has plenty of options. The Hellenic
Duty Free has all your standard necessities, and other shops specialize in cigars, jewelry, perfume, and sunglasses. If you really want to splurge or put give your credit card a workout, check out high-end boutiques like Michael Kors, Salvatore Ferragamo, and Max Mara.
- Spa Massage
If you’re in need of some pampering, the spa inside the Sofitel hotel is open to non-guests. Services include facials,
massages, manicures and pedicures, and more. Note that the Sofitel is located just opposite the airport terminal, so you’ll have to exit and re-enter Security.
- Get online
Stay connected to friends and family, update your social media accounts or surf the internet courtesy of the airport’s
free WiFi. You’ll want to use your time wisely though, as there is currently a 45 minute time limit restriction. Boo!
Uninterrupted, premium options are available for a cost.
- Sleep
When it’s time to catch up on some Z’s, there are plenty of stiff seats and benches. Travellers try to camp out
overnight, but the airport isn’t always friendly to them – sometimes playing loud announcements or waking up anyone who’s dozing. For better quality sleep, you’ll have to shell out some cash – a Sofitel is located just opposite the main terminal, with day rooms available from 12pm – 6pm. Several other hotels are located within a few minutes’ drive, with some providing free airport shuttle service. For details on locations, shuttles, and day rooms, see our Athens Airport Guide.
They also include an Athens Airport Guide for more information about more services and facilities available, such as food, WiFi, mobile charging, luggage storage, nearby airport hotels, and much more
And if you really want to leave the airport to go sightseeing, I would suggest avoiding Athens all together and going to Sounion, which is about 45 minutes/46 km away, to see the Temple of Poseidon, where according to the myth, this is the site where Aegeus, king of Athens, fell into the sea because of a misunderstanding. This is where the Aegean sea earned its name for centuries to come.