I've been in Turkey a couple times during Ramadan and will say that as tourists in Istanbul, Cappadocia and "someplace on the coast" you will scarcely notice anything is different. That said, I personally try to refrain from drinking or eating in public--especially towards the end of the holiday--and I also did my best to follow the fast for about a week one year. I succeeded save a few swigs of water one especially hot and sunny day when we'd been touring on our feet since early morning. I sincerely don't know how some outdoor workers survive. Non-Muslims are under no obligation whatsoever to obey the fast but especially towards the end of Ramadan when it occurs during the long, hot days of summer people can get rather testy and resentful. Consuming food/drink in a bus during daylight is probably the worst faux pas and can earn you some nasty looks. Most restaurants will be utterly jam packed right after sunset so it's best to avoid that time.
If you are in Turkey anytime from say Thursday, July 16 through Tuesday, July 20 you can expect some travel impacts. Worst is either getting out of any large city at the beginning or getting into any large city at the end of the holiday. The days dead in the middle however are typically very slow as everyone is at their destination. You can also expect general tourism by the Turkish to pick up greatly around and for some time after these dates as many avoid taking holiday during Ramadan.
Beyöğlü and Sultanahmet are generally the most convenient areas to stay in as tourists. Sultanahmet is essentially on top of many of the major sites of the city. Personally I find it too touristy and somewhat difficult to find good food at a reasonable price--it is however very convenient especially if your time is short. Much of Sultanahmet will seem nearly deserted at night.
Beyöğlü (especially within a few blocks on either side of Istiklal Caddesi) is also very popular with tourists but it is equally--if not more--popular with the Turkish as well so it feels decidedly more "Turkish". There are innumerable places to eat, drink (anything), shop, smoke, dance, etc. and it's easy to find good food at a reasonable price. Alcohol is rather expensive in Turkey--particularly in night club and always for imported liquor/wine. The popular local beer, Efes, is a decent pilsner that is an especially good value when served on tap. There are also some excellent Turkish wines at low to moderate price. If you stay in Beyöğlü I suggest finding a hotel fairly close to either Taksim Square or Galata Tower as both have one-stop subway lines leading down to the tram line that takes you across the Golden Horn to the Sultanahmet area. The north side of Istiklal Caddesi near Taksim Square has a great number of bars and clubs that rock LATE and LOUD into the night--especially weekends. Keep that in mind when choosing accommodation.
During July nearly any beach within a hour or so by land of an international airport (Izmir, Bodrum-Milas, Dalaman, Antalya and Gazipaşa) will be crawling with tourists--most of them from western Europe and a great many of those on cheap package holiday at all-inclusive resorts. When touring on your own it is rather difficult to find suitable beach accommodation--particularly when your time is short. Your cost of one night at one of the resorts that caters to inexpensive package holiday goers may cost you as much as they paid for one week! Getting away from such usually involves quite a bit of transport time and/or significant expense for accommodation.
You can find some fair beach places near Izmir--Çeşme and Kuşadası are the closest. Çeşme hasn't been overtaken by the package holiday trade (but it can be rather expensive) while Kuşadası is nearly on top of the ancient city of Ephesus. Flights between Izmir and Istanbul and fast, frequent and inexpensive and you can also get direct flights between Izmir and Kayseri (Cappadocia).
Antalya is a city of more than a million with tourism the only industry. There is a lot to see and do in the general area and the "soft stone" (the only way I know to describe them) beaches are incredible. Old Town Antalya, Kaleçi, retains a bit of authentic charm but alas there are no beaches as it surrounds a small harbor. If you choose carefully you can find a nice place for a few nights in/around Antalya without either ending up in a package tourist, cookie cutter hell-hole or spending a fortune. There are also direct flights between Cappadocia and Antalya.
I suggest you make any necessary domestic flight reservations ASAP! I also suggest that you make hotel reservations for everyplace you intend to stay very soon as in my experience the best value places in Istanbul, Cappadocia and most coastal destinations tend to fill rapidly during high season!