Depending on your passport you can cross the border and head over the Ercan airport ( ECN ) from there you can catch numerous flights to IST.
There are several taxi companies that have the licence and insurance to do so, it will cost yo ua few $$$ but beats flying via ATH.
All UK, US, AUS, EU passports should be ok to cross, as long as you do not need a visa to enter turkey.
Good luck