Both very cool places, and very different.
Second the suggestion for ice cream in Istanbul. Also get some donair kebab, street-meat style.
For Dubai, consider renting a car. I believe the train is running now (wasn't when I was there) so check into that. I remember the city being very spread out, and much bigger than I realized, without much option to get around. Car rental was very cheap.
Enjoy the trip!
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