There was a post on this a little while ago, but I can't find it.
Lykia2go is a good shop, I have bought 2 Salcano bikes there, the owner speaks good english. This is along the main road between Calis and Fethiye.
Also along that road, opposite the Zakuum restaurant is another shop. The owner and his wife run the Fethiye cycling group. He has a good range of bikes too incuding Specialized, Scott and Giant, selling urban, road and racing bikes. I use him now to service my Scott and have been happy with his service. He is Romanian and speaks a little English and would recommend this shop.
The prices for both shops compare with UK prices, but the after sales (service etc) are considerably better value than the UK. If you are looking for a decent bike and a good choice, then I would have a look at both of these shops. Otherwise there are bike shops both in Fethiye and Calis that sell cheaper makes, which are basic, lower quality, so it depends on how long you want to the bike to last and what you need it for.