Çukurcuma Square is a favorite destination for antique lovers, in Istanbul. There are loads of shops in the nooks and crannies of the narrow streets feeding into the square. You can find old and new furniture, accessories, paintings, carpets, and all kinds of fascinating little artifacts. Also, these;
Horhor Bit Pazarı (Flea Market)
It is very difficult to find this market, but the reward is well worth the effort. This is a flea market with seven stories and two hundred twenty shops filled to bursting with furniture and collectibles.
Mecidiyeköy Antikacılar Çarşısı This immense building in the heart of Mecidiyeköy is packed with refined antique shops that sell old and new decorative accessories and furniture.
Üsküdar Antikacılar Çarşısı It is located just behind the Municipality Building in Üsküdar. There are about forty stores offering antiques 80-160 years old and antique pieces from Europe and the Ottoman Empire. You can also find old but not antique pieces at reasonable prices.
Kadıköy Antikacılar Çarşısı Kadıköy Antikacılar Çarşısı is located at a multiple story building at the beginning of Moda Caddesi. However many antique dealers have shops at both Moda and Dr. Esat Işık Caddesi and the narrow streets opening to those avenues, such as Tellalzade, Sakız. Many old objects besides antique pieces are available. You may be pleasantly surprised by the wide range of attractive goods!
Antiques can be an outrageous price. Sometimes it helps to look locally and you are in Datca so there could be some interesting stuff in the villages around you, try asking the locals carpenters, they may be making new furniture to replace old. Just a tip, ask for things that are "eski" (old) rather than things which are "Antik" because as soon as you attach the word Antik to something the price quadruples.
I once spent several hideous days in Izmir looking for old doors and hitting my head against a brick wall would have been more rewarding. In the end I learnt eski kapi would have been the thing to ask for.
There is a huge architechural salvage place near Capadoccia but it would mean taking a van and driving for two days to get there. If I ever do another renovation project that would be where I would go though.