My wife and I are taking the Best of Turkey tour in May and will arrive a couple of days before Rick Steves' starts. Any recommendations for daily tour bureaus or agencies that organize tours for sights other than the ones we'll see with RS? Thanks.
You can take a tour if you prefer, but Istanbul is very easy to see on your own; the tram goes almost everywhere you will want to see. You'll be getting a copy of Rick Steves Istanbul with your tour materials, and it has all the information you need.
I see from the tour page's "Pre Tour" tab that the following sights in Istanbul are not included in your tour: "Istanbul Archaeological Museum (includes Tiled Kiosk and Museum of the Ancient Orient); Yerebatan Underground Cistern; Çemberlitaş Hamam; Mosque of Süleyman the Magnificent; Galata Tower; and Dolmabahçe Palace."
Of those, I saw the Underground Cistern, the Süleymanye Mosque, and the Dolmabahçe Palace, and recommend these if they interest you. I also enjoyed the Jewish Museum (in a synagogue), a day trip to Kadıköy on the Asian side, the modern art museum, and some of the other mosques (the New Mosque and Rüstem Paşa Mosque, for instance, are not too far from each other, but are different both from each other, and from the Süleymanye and the Blue Mosques).