I will have 6 nights in Istanbul at the end of 3 weeks in Turkey.

Should I do 3 days at the start and 3 days at the end instead?

No. Keep your six days together - Why go back and forth to the airport twice and check into and out of hotel twice?

Or... you can use the first 3 days to get acclimated to the timezone. I believe it's 7 hours ahead of EDT, which means it's 10 hours from where I live on the Left Coast.

The 3 days at the end can be used to settle in, regroup, catch the things you missed, and relax your mind for your trip home.

There is a feeling of knowing more about Turkey and then looking at Istanbul in a somewhat different manner. That would argue for splitting the time.

For us, an immediate transfer to a flight for Ismir would not have worked particularly well because we arrived in one airport and left from another.

Good question, Rastaguytoday makes a good reason for doing the 3 days at the beginning. I am inclined to agree altho Sassafrass is being more logistical. We do not know how far away you are flying from and if that will involve a loss of catch up time?

There is a lot to do in Istanbul! Depending on where your next stop is, I would consider keeping the Istanbul days together. Taking into consideration the jetlag factor, as others mentioned, Istanbul is a lot of hustle and bustle - so if your next stop is more leisurely and you think it would make it easier to acclimate there, put all 6 Istanbul days at the end then. However, if I decided to split the days, I might consider doing a 4-2 split. As I said, lots to do there! So, maybe better to do on the early end when you have lots of energy and use last 2 days to do stuff you missed, like shopping or finding good weather for a cruise on the Bosphorus.