My wife and I have just returned from a wonderful three week trip in Turkey: Istanbul (4 days), Cappadocia (one week), the North Aegean (6 days), and Istanbul (3 days). Although I intend to submit a trip report I thought it might be useful to share some tips that helped us get the most out of our trip.
1. CityMaps2Go. I can't say enough for this smart phone app. It allowed us unbelievable freedom to go where ever we wanted: strolling through the fascinating Fatih district of Istanbul, exploring the many valleys and canyons of Cappadocia, even showing the map to bus drivers to make sure we were on the correct bus route. Besides giving you your current location the app also has Wiki write-ups for thousands of buildings and ancient sites. We'll be using this app for all our future overseas trips!
2. Istanbul Kart. This public transportation pass makes getting around Istanbul much easier. You can place the card on a kiosk and see how much money remains. One card is all you need for a family; just swipe the turnstile with the card for each person in your party.
3. Museum Pass. Not worth the price IMHO. To our surprise it only allows you to enter a museum or attraction once. We did not get our money's worth (currently 85Tl).
4. My wife kept a light-weight scarf in her purse all the time for entering mosques.
5. Cameras and binoculars. I debated whether or not to take my large camera (1200mm zoom) or a point-and-shoot. Glad I decided on the big camera as Turkey is a photographer's dream come true. Small binoculars are handy for looking at mosaics and frescoes on church or mosque ceilings and distant walls (e.g., terrace rooms at Ephesus).
6. If you plan to spend a lot of time touring Greco-Roman ruins you might consider taking a small collapsible umbrella to shade you from the punishing Aegean sun.
7. Language skills. As independent travelers we often find ourselves in places where some language skills are helpful. Even if that's not the case for you a few Turkish words and phrases are nice to have -- and are met with big smiles by the recipients!
8. Smart phone usage. We chose to go with Verizon's Global Data Plan which ran us $52. Although not cheap we had the peace of mind knowing we wouldn't get one of those huge phone bills you read about. There are other options for using your phone in Turkey (discussed in detail elsewhere on the web).
Iyi yolculuklar!

I commend your wife for carrying a scarf.

I saw a couple of French women - fierce advocates of "le laicisme", Republican secularism, it seems - who turned away haughtily when an attendant tried to hand them scarves in the Suleimaniye Mosque. I would have b**ch-slapped the pair of them.

Thank you so much for taking the time to share this.

My wife found some great (cheap... well under $5US) in many of the little markets in some of the towns. She picked up a couple so always had ones for the mosques.

I'll take the opposite on the Museum Pass. We got good value out of it and it allows you to skip the lines!

Thanks! I can't wait to hear about your 6 days in the North Aegean!

Very helpful, thanks.

Thanks for sharing!

I also thought the Museum Pass worth every penny. For me, it was just barely more than the individual admissions would have been, and as astein12 noted, I was able to bypass all the lines -- priceless!

I'll just chime in to agree with those who found the Museum Pass to be well worth it...even had it not been financially beneficial, which it was after just 3 visits.