We just returned from a cruise that also included an overnight stop in Istanbul and one day at Kusadasi. Here's what we did and what I'd do differently:
We decided to spend the night off the ship. You certainly don't have to -- I just wanted to feel like I'd really spent time in the city. I'd do it again, but really the ship is quite close to the heart of the city so it's not necessary.
We docked at 1:00 in Istanbul. I thought there may be a delay getting off the ship because the Turkish authorities had to board and do some paperwork and landing cards had to be delivered to every cabin. I was wrong -- we were cleared to disembark almost immediately. If you want to be ahead of the excursion groups to leave the ship, be ready to go right at 1.
After a *lot* of thought and discussion between the four of us travelling together we decided to go on our own for the first day and hire a private guide + transfer for the second day (NOT through the ship which was crazy expensive).
We left the ship, walked out of the port and were immediately assailed by beggars, touts and assorted "salesmen" while we withdrew our cash from the ATM. (Which by the way is at the exit of the port, turn left and it's there on your left.) We didn't have our bearings and weren't sure which way to go to get on the tram to take us into Sultanhamet but a backpacker pointed us in the right direction (which is to continue past the ATM. A few blocks down is the tram stop. You buy tokens at the booth and use them to cross into the tram waiting area.
We took the tram (crowded but air conditioned) two stops to the Spice Bazaar which was incredible. But if your time is really limited and you plan to go to the Grand Bazaar, you could skip it as it is very similar.
Then we took a taxi to our hotel. Mind you, we've been to 20+ countries on nine trips now, and should know better, but we got totally taken. He charged us 20 lira and dropped us in a random spot nowhere near our hotel. He indicated hat it was a short walk down the street and pulled away. If you take a taxi, make sure you are *at* your destination or consult a map to ensure you are close (some areas are legitimately pedestrian only) before you pay.
We checked into our Hotel, the Dersaadet, which was staffed by very friendly and helpful employees.
We walked then to Hagia Sophia, not to be missed, the Basilica Cisterns, also amazing, and the Grand Bazaar, another incredible highlight. Then we walked back to our hotel to deposit our packages

and took a taxi (that our hotel called for us) to the Beyoglu district for dinner at a "meyhane." This taxi was less than 10 lira for twice the distance.
After dinner we hailed a taxi and directed him to take us the the Blue Mosque -- this way we knew he couldn't trick us. From here we were a 5 minute walk form our hotel but my companions were hesitant bout walking the dark streets. (I didn't feel unsafe at all - maybe a matter of perspective).
In hindsight, given how much time we lost looking for our way and trying to find the hotel, I would hire the guide for the entire time. It is really quite reasonable.
The next morning we met our guide and he walked with us to the Blue Mosque and Topkapi Palace. I can't imagine not visiting these two sites. I was very displeased though, that the guide cut our Topkapi visit short to take us to a ceramic shop (sales pitch

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Then the driver picked us up and drove us back to the ship.
I feel like we saw a lot in such a short time but it would have been less stressful with a guide the entire time. I would not have considered a ship tour -- I very much want to do what *I* want to do and hate being in a crowd following the leader.
Here's a
photo journal of our visit to Istanbul In Kusadasi we booked a guide and driver for the entire day. We visited Ephesus (took about 2 hours), had a leisurely lunch, went to a museum, visited St John's Basilica and went to a small village to find a spoonmaker my friend had read about. We easily fit all this in and had a little time in port for some tasks (like calling home). Here's
the photos from that day.
This can in no way be considered slow travel but I know now we want to return to Turkey, especially Istanbul.
I'll be glad to answer any questions.