Athens

The greatest symbol of the glory of Ancient Greece, the Acropolis rises spectacularly in the centre of Athens. In the reign of Pericles, in the 5th century BC, the hilltop was deemed a religious sanctuary. Just as pilgrims of millennia past made their way to worship here, you can ascend the marble steps on the west side, to find yourself dwarfed by the towering columns of the magnificent Parthenon. Complete your experience by seeing a concert or play at the Odeon of Herodes Atticus.

Natural light cascades through the spacious galleries of the modern Acropolis Museum, illuminating the priceless treasures that have been removed from the hill and installed here for safekeeping. The pinnacle of the museum is the top-floor glass atrium, where the 161m-long frieze from around the top of the Parthenon (minus the portion still held in the British Museum) is installed at eye level, so visitors can see all the details of this masterpiece in marble, and get a truer sense of its grand scale.

Follow in the footsteps of Socrates and his various political and philosophical cohorts at the Agora, the heart of ancient Athens' civic life and the birthplace of democracy. In the stately Stoa of Attalos (an architectural paradigm for shopping arcades that you'll recognise across modern Athens), the Agora Museum displays unusual finds from ancient daily life. The Temple of Hephaistos is exquisite and very well preserved; see how many of the Labours of Hercules you can identify on the frieze.

Athens' preeminent museum houses the world’s largest and finest collection of Greek antiquities. Priceless items date from the Neolithic Era (6800 BC) to the Cycladic, Mycenaean and Classical periods. It's gratifying to stroll the galleries and realise just how many of the finely wrought sculptures look familiar, just because they're cornerstones of Western art history: the bronze figure of a bearded god, say, or the hammered gold death mask of (maybe, maybe not) Agamemnon. Among such icons are plenty of other surprises; don't miss the frescoes from Santorini upstairs.

Greece's largest temple was seven centuries in the making. Or rather, what used to be Greece's largest temple – today only a handful of its colossal columns remain, as the rest were picked apart and reused in other buildings. The temple was dedicated to Zeus, and, unofficially, to the Roman emperor Hadrian, who actually finished the construction job and erected a statue of himself. While you're here, note Hadrian's Arch, congratulating him on his achievement. And explorers can seek out a sanctuary to Pan, on the far side of this site.

This impeccable private collection shows the spectrum of Greece from ancient times right up through the mid-20th century. It occupies a stunning neoclassical mansion, with fine art and mundane folk objects – both equally beautiful – displayed chronologically. As a kind of counterpoint to the pure classicism celebrated elsewhere in the city's archaeological sites, the Benaki collection tells the story of how Greece has absorbed foreign influences and ideas to create its uniquely syncretic culture. If you have time for only one museum, make it this one.

The city's ancient necropolis is home to the Street of Tombs, where classical VIPs were interred. Many of the finest grave markers are replicas; the originals are on display at the absorbing small museum on-site. The area was also the ceremonial entrance into ancient Athens, and while the gates no longer stand and the arriving road is now a paved city street, it's still an interesting place to pause and imagine the activity that would've taken place at the gates here.

The mythical battleground of Theseus and the Amazons is a green park studded with small ruins connected by beautiful stone paths that are themselves a minor architectural marvel. Make time in your schedule to come here – and to the neighbouring Hill of the Pnyx – around sundown one evening to watch the lights on the Acropolis switch on and glow gold against the blue sky. More prosaically, this is also where a lot of Athenians walk their dogs, so you'll be out strolling with some great Greek pups.

One of the great pleasures of the Athens summer is seeing a film in one of the city's many outdoor cinemas. Grab a beer at the concession stand, settle into a comfy lounge chair and enjoy the magic of the silver screen. At some of the best and oldest movie theatres, such as Cine Paris in Plaka, you may also enjoy a view of the Acropolis alongside the latest Hollywood blockbuster or black-and-white classic. Screens start opening in May and usually run through September or October.

A contemporary Athenian wonder, the Stavros Niarchos Foundation Cultural Center designed by Renzo Piano is home to both the Greek National Opera and the main branch of the National Library. Seeing a performance here will be a highlight of your trip, but there's plenty of free things to do and see as well, including meandering through the stunningly beautiful Stavros Niarchos Park. Designed to showcase Mediterranean flora, the gently sloping gardens are the perfect spot to relax and take in the views and cooling sea breezes.