To the east of the Acropolis, the Zappeio Gardens and the ruins of the Temple of Olympian Zeus lead to the elegant Panathenaic Stadium, built into Ardettos Hill. The attractive residential districts of Mets and Pangrati surround the stadium to the southwest, east and north. Mets, named for a brewery once headquartered here, is characterised by some delightful neoclassical and prewar houses; Pangrati is a diverse, unpretentious residential neighbourhood with low-key-cool places to eat.
The Temple of Olympian Zeus is the main archaeological site here, and although it covers a large area, it's not filled with a lot of detail, so you only need about half an hour or 45 minutes to stroll around. If you're feeling particularly pressed, just peek from the fence by Hadrian's Arch.
Likewise the Panathenaic Stadium, where what you see from outside is pretty much what you get inside past the gate. Still, if you've ever been competitive, it's a thrill to be on the track.
Really, the life of these neighbourhoods are both uphill a bit. Unwind on Plateia Varnava, have lunch or a coffee up here, and then stroll over to Athens' First Cemetery, where Greek luminaries are buried in elaborate tombs.
There are two destination restaurants in Pangrati (Spondi and Mavro Provato), and the former is on the dressy side, which makes it tricky to combine with earlier sightseeing. You'll probably just have to make a special trip (taxis are cheap, remember). You could possibly combine the outing with a show at the good jazz club in Mets, or a show at the cinema in Zappeio Gardens.
- Panathenaic Stadium Jogging around the track with the roar of the (imaginary) crowd in your ears, and posing for a photo on the Olympic medalists' stand.
- Athens' First Cemetery Admiring the work of some of Greece's finest neoclassical sculptors, which just happens to top the tombs of the city's rich and famous.
- Temple of Olympian Zeus Counting columns at this enormous fallen temple, which took many centuries to build and just as many to reach its picturesque current state.
- Hadrian's Arch Saying thanks to Hadrian yourself at this pretty marble monument to the Roman leader who added so much to the Athens cityscape.
- National Gardens Wandering in this shady park, and maybe taking in a movie on a summer night in neighbouring Zappeio.
Pangrati's Plateia Varnava is a great place to experience a typical Athenian neighbourhood, with families dining in the tavernas and kids playing in the square. Buy a snack and a soda from the periptero (kiosk) and sit and enjoy the scene.