Would a private taxi be prepared to do this and at what cost ? (from google, seems the rate is Eur100)
Is there a (regular) bus?
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You can take a train; it will be ideal for you, take a taxi from the airport to the train station in Ramses or in Giza, it should cost not more than 13 Euro and then take the train to Port Said, according your arrival time the streets might be crowded but it's a much more comfy trip.