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.