There are many places in Fethiye to get air con units from. From Migros to Eren Spot to the main electrical outlets and there are some shops that just do air con units.
Migros (or the supermarkets) offers are fairly reasonable pricewise and they fit for you but they are more the budget range. I fitted Daikin air con units in 2004 and they have been great until last year when 1 blew its main circuit board and it was only another £100 for a complete new unit rather than repair. I would go for a known brand ie Toshiba, Daikin, LG/Beko, Mitsubishi etc. rather than an obscure brand never heard of so you can get spare parts if you need them. I would also go for unit that heats and cools so its good for the winter and an 'inverter' model as they are cheaper to run than a basic on off model all be it they cost more in the outset. Shop around dont just pay the first price you are given.