We booked private excursion with fellow cruisecritics members.
The standard sites are covered by the tour. For the DIY, it's perfectly doable as the sites are very close to each other. the problem is lining up for tickets. Our guide has his short cut though.
All guide will like to take you to some kind of carpet demo/shopping, it is a sales pitch and take up time, best avoid them if you are not interested at all. We went to one, almost about to test the limit of my AMEX card. Have to say that the Turkish carpet is really work of art.
Back to ship for dinner and walk to Galada bridge afterward, about 20 minutes walk. Street is safe and full of cafes.
Take the tram to the Spice Barzzar next morning, 2 Lira each way, 3 stops and only one line, can't get lost.
IMHO, the Spice Barzzar is much better than the Grand Barzzar, easier to navigate and much interesting to see.
Outside the Spice Barzzar there's a few 'fishing boat' selling local fish sandwiches, try this. It's pan-fried fish on a bun and a pinch of salt.
Super friendly people (some don't speak English), aggressive sales people try to sell you anything.