We fly in to Athens airport at 2 am. Does the E95 bus run all night? Is there any way to avoid paying a fortune in taxi fare? We are a family of 4.

The E95 bus runs about every 20 minutes all night long and costs 2.9 euro per passenger to Syntagma Square. You'll pay the driver and then put your ticket in the validation machine onboard. There's a luggage rack on board the bus for all your bags.

Thanks for the answer!

An approx. cost of 30 to 40 euros for a taxi drive is not.. a fortune,and you will reach your place within 30 minutes.
Consider the cost of 4 bus tickets,and how are you going to reach your final destination from the bus terminal?by taxi?

If you do decide to take a taxi from the airport be sure you understand the total charges which will include surcharges for extra bags and a late-night fee BEFORE you accept the ride.

Taking the bus into town to Syntagma and then a taxi to your hotel if it's not within walking distance will be a lot cheaper.