I can only provide some perspective on Istanbul.
Sites:
We had a private tour guide for the following two tours, but there are likely small group tours with similar itineraries.
We toured the Old City "must see" sites which was great if you can only do one tour. Topkapi, Hagia Sophia, Blue Mosque, Cisterns, and "meatballs" at Tarihi Koftecisi or someplace similar (meatballs are still a form of kebabs).
Having said that, my favorite tour was off of the beaten path. We took a ferry from Karakoy to the Golden Horn and then did a walking tour through former Greek and Jewish neighborhoods (Fener and Balat). We stopped at Greek/Armenian/Bulgarian churches (including the cast iron church), the Patriarche, the "bluest mosque" (Rustem Pasha), and ended at the spice bazaar in Eminonu (historic center). This tour walks you through centuries of religious, and political, transitions while exploring neighborhoods of the city you may not otherwise visit.
Turkish Bath: Kilic Ali Pasa Hammani
Our tour guide said this is one of the top two places for a Turkish bath. I recommend it - definitely something to experience at least once in your life.
Restaurants:
Ala Rasi (near Taksim Square): incredible Afghani/Pakistani/Turkish fusion restaurant.
Develi: a few locations in Istanbul, I went to Etiler. Traditional Turkish Mezze and Kebabs, but more "upscale" (still casual) so go with the higher end meats and lamb versus the traditional kebabs throughout the city.
Sur Balik (Arnavutkoy location, but they have others on the Bosphorus): good seafood with great views.
Livar Balik Eli: more casual than Sur Balik with even better seafood (a couple of blocks from Sur Balik), but not as nice of a view depending on your table.
Ali Muhiddin Hac Bekir: the gold standard of Turkish delights with a few standalone storefronts in the city. Don't buy the delights on display in the bazaar that everyone has coughed and sneezed on.
The walk between Kilic Ali Pasa and Taksim has a lot of cool cafes and bars (along the triangle of: Bostanbasi, Yeni Carsi, Hayriye - and then towards Taksim). Walk up, or easier down from Taksim, and meander along the side streets in the evening. Ala Rasi is near this area (10 minute walk).
Besiktas is well known for dining and lively streets. Ciragan Palace Kempinski (a hotel next to the Four Seasons) is nearby and a nice place to stop for a tea while enjoying a view of the Bosphorus.
Kadikoy on the Asian side has a lot of restaurants, bars, and is a good place to check out (plus a Bosphorus crossing on a ferry).
However you choose to get onto a boat on the Bosphorus (ferry or a Bosphorus tour), you need to do it. It gives a really unique view of the city and a feel for why Istanbul has been such an important/crucial city for different empires over thousands of years.
Airport: If you're flying Business Class on Turkish Airlines, then get to the airport early (minimum 3 hours before your flight). By the time you go through security to enter the airport, security after check-in, and security again at the gate just before boarding - your lounge time will be limited. Their lounge is up there with the Asian airlines (reminded me of a modern themed Thai Airways lounge in Bangkok). Huge, and busy lounge, with fantastic food. The lounge alone is a destination in Istanbul.