Few cities in the world are as historically significant as Athens, Greece – the cradle of Western civilisation and the birthplace of democracy.

And yet Athens makes few travellers’ top ten lists. Though it has the history to match, the capital of Greece seems to lack the romantic lure that makes Europe’s other great historical cities – such as Rome, Istanbul and Naples – so popular.

That’s a real shame because Athens does have a lot to offer its visitors, besides being a gateway to the remarkable Greek Islands. These are five of the best things to see and do in Athens, Greece.

Visit the Acropolis

Overlooking the chaos that is modern-day Athens is one of the most picturesque of the city’s remaining ruins – the iconic Acropolis of Athens.

A UNESCO World Heritage Site, the Acropolis is an ancient citadel made up of a number of temples that date back to the Bronze Age. The most famous symbol of Greece and arguably the most significant of these ancient ruins is that of the Parthenon (pictured), a temple dedicated to the goddess Athena.

Entrance to the Acropolis costs €12 (£10/$16 US); the hill can be a bit of a tough climb when the weather is at its hottest but it is most definitely worth it for the view over Athens alone, let alone all the photo opportunities.

Experience the Agora

The ancient Agora was the commercial, religious and political centre of ancient Athens; now it’s one of the best things to see in modern Athens.

Strewn with fallen columns, this (relatively) green space is where Greek philosophers such as Socrates and Plato came to make speeches and dispense wisdom. It’s essential viewing if you’re a fan of classical history.

Go to the best open-air cinema in Athens

Apparently Athens has more than 15 open-air cinemas where cinephiles can catch the latest films under a starry sky – but surely none are as cool as the Cine Thisio.

Built in 1935, the Cine Thisio is the oldest outdoor movie theatre in Athens and boasts an amazing view of the Parthenon, which lights up at night. Even if you don’t enjoy the movie – I saw Mama Mia! here in 2008, which was apt because we were heading to the Greek Islands the next day – you’ll enjoy gazing up at the Acropolis.

Don’t trust me? CNN Travel ranked the Cine Thisio one of the 10 best movie theatres in the world.

Climb Mount Lycabettus

For the best view over Athens you’re going to want to climb to the top of Mount Lycabettus, a 277m (745ft) mountain with clear views over the Attica basin and the Aegean Sea. Or you can do as we did and catch the funicular (or cable-car) up to the top.

Eat gyros!

Great news for budget travellers to Athens: Greek gyros are cheap and delicious.

A Greek dish of meat roasted on a vertical spit, gyros are very similar to Turkish doner kebabs except that they most commonly have Greek tzatziki sauce on them – sort of like yoghurt mixed with garlic, salt, cucumber and olive oil – and French fries inside them.

It may not be the healthiest meal in the world, but this Greek fast food is very inexpensive – just a few euros each – and they certainly hit the spot after a big day of sightseeing in Athens.

What do you recommended travellers should do in Athens, Greece?

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