We took a taxi from the airport to Piraeus (the Port) and it was 45 minutes.
It's a long story but originally we were going to stay at the Intercontinental Hotel close to the Acropolis and I was told it would have taken 30 minutes to Piraeus by taxi depending on traffic.
Something you should no is that until the Olympics next Summer Athens is one big building site! The amount of roadworks and noise, dust and dirt that we saw from the airport to Piraeus was awful. Luckily it wasn't our first impression of the place as we had enjoyed a stay before.
Taxis are indeed readily available, but you MUST agree a price with the driver before setting off. We tried to and still paid slightly over the odds, but we heard nightmare stories of others getting REALLY ripped off.
If you need a hotel recommendation, the Athens Intercontinental is great albeit expensive with views of the Acropolis from some rooms and it's upper floor restaurant, (my company paid last time).