You can't go to Athens without seeing the Acropolis but skip the queues and go against the massive tourist flow (yes, even in 35 degree C heat, there'll be crowds) by starting your day at Hadrian's Library. Buy a multi-site ticket to Athen's Archeological sites here without a queue and you'll get your ticket to the Acropolis included (€30, summer 2017). The Library itself is worth a quick explore, particularly the small museum (which also offers air-con relief from the sun).
A short walk from Hadrian's Library, the Agora is a wonderfully kept ruin. Included on the multi-site ticket, it's worth the visit and is much less visited than the Acropolis. Explore the Tower of the Winds - as well as providing a shady respite, marvel at the combination of sundials and wind vanes.
Building up to the Acropolis, keep the ancient history coming with a stroll through the Ancient Agora, including epic panoramic views from the heights of the Temple of Hephaestus (pictured below) across the city. With plenty of trees and benches to provide a brief sit down, this is a place where you can find your own quiet corner in the busy city.
Grab a Mythos
Recoup from a busy morning with a stop at one of Athen's many restaurants. For beer drinkers, grab a Mythos and make sure you rehydrate with plenty of water. I can't remember the name of the wonderful place I stumbled across (on a hill; the chair had different length legs to 'even' it up with the slope of the hill!) but look for somewhere where the locals are dining. One Greek salad and starter of calamari was enough between two hungry explorers!
Call me crazy but as the morning's crowds are departing and the sun is at its peak, is a fabulous time to explore the Acropolis! You'll get sweaty and happily hide in the slim shade of a sapling, but it's worth it. I doubt there's ever NO crowds at the site but you can skip the ticket booth (wave your pass at the gate attendee) which will save you time. We went up the South Slope entrance - a longer walk but picturesque, and makes the Parthenon worth the effort. It also allows you to stop and marvel at other Acropolis sites including the exquisite Odeon of Herodes Atticus, still used for outdoor concerts.
Your ticket doesn't include entrance to the separate Acropolis Museum so if you want to stop off indoors for a change of scenery, it's worth the extra cash but if you're feeling fine and want to keep walking, stroll past the Museum towards Hadrian's Arch (amongst the traffic; no ticket required) and the Temple of Olympian Zeus (included on multi-site ticket). Stock up on water; nice and cold bottled water is available for a bargain price at all sites in vending machines.
To finish your epic walking tour through Athens' history, finish up at the Panathenaic Stadium - believed to be the only stadium in the world built entirely of marble. Not included on your ticket, you can either view the stadium from the road or pay the entry fee. There's been a stadium on the site since 330BC and was used as the opening and closing ceremony venue, plus 4 of the 9 sports, for the first modern Olympics in 1896.
After arriving in Athens around 2am and a brief sleep, we explored all the above in around 8 hours without ever feeling hurried. From there, we headed to the Athens Riviera for some R&R for a few days - a great way to meet locals and chill without having to fight tour packages on the main Greek islands. Wherever you go from Athens, enjoy!