Didim is your best bet Scone1. Several shops sell them there, try the hardware shops.
Haven't seen any for sale in Akbuk but you could try the Japon Pazari in the centre of town, he has all sorts of stuff there, if anyone sells safes in Akbuk it will be him.
Hi we bought one in Didim main street just near the traffic lights last year from the hardware shop just opposite Vestal who sell electrical goods and ozzies bar is next door to vestal.
I believe we paid about 150 lira plus 30 for delivery stands about 2 foot tall by 18x15 inches at a rough guess.
We priced one from another shop same size but different make and that was 7 to 800 lira.
For us we think its safe to have one (excuse the pun ) it took 2 men to carry it to the second floor stopping several times to catch their breath, we spend about 6 to 8 months a year in the apartment and only use it then.
We leave it open when we are back in the UK. ( plus our apartment block is occupied all year round )