Lavrio in southerneast part of Attica region, about 60km southeast of Athens and 12km NE from cape Sounio.
On the pic you can see the map of Attica region where I highlighted LAVRIO, ATHENS, PIRAEUS, SOUNIO, RAFINA and the AIRPORT.
We usually drive there via Lavrio avenue but you can also go through Attiki Odos or the coastal highway Athens-Sounion through Glyfada (but this one make sense only if you want to check beaches like Saronida, Anavissos, Legrena).
The a suburban bus (KTEL) departs from Athens at Pedion Areos (3’ away from Victoria metro station). The ticket costs 5euros but the ride is long and boring with many stops (about 120’ from Athens!). The first bus departs at 5.45am and then there’s one every 30’ (60’ during weekends)
A taxi ride from Athens will take about an hour and will cost about 70 euros,
From the airport
From the airport you can take taxi (50euros) or wait for the bus (4euro), the first one departs at 6.30am and then there is one every hour more or less (the last one at 22.00). The bus stops at Markopoulo where you take another bus.
From Lavrio you can catch ferries to Kea(Tzia), Kythnos, Lemnos, Agios Efstratios, during summer months to some other islands of cyclades too
Some old greeks remember the train that connected Lavrio with Athens city cennter. It was in use from 1885 to 1957, a train line that was 67km in lenght. The newspapers wrote about a reactivation of the train line in the future, it will reach Koropi station near the airport but now with the economic crisis the plan was left behind.
You don’t really need anything here, just walk around in this small town.
Obviously a car will be very helpful to check the area around, you can visit some nice beaches or the famous cape Sounio (11km away from Lavrio).