I'm not sure I'd go stay overnight outside Istanbul.
I flew into Izmir from Istanbul and then rented a car to see Ephesus...stayed in Selcuk and Sigacik. That was great....but it took most of a day traveling each way.
Princes' Islands...I've heard good things about it.....will only take a portion of the day.
Do the Bosphorus strait ferry cruise. That will get you out of the city.....do it on a nice day though. I did it on a overcast day and it took much of the enjoyment away. The small towns along the way aren't much but it gets you away from Istanbul for a day..and on the water.
Go across the strait to the Asian side of Istanbul.
The favorite city of a friend of mine who has traveled to Turkey 3 times is Bursa...but it's far away.
My thoughts...assuming you're flying back to USA from Istanbul...
If you were to travel........day 1 arrive in Istanbul, day 2, 3, 4 stay in Istanbul....day 5 travel to another location and stay overnight...day 6 stay in the location....day 7 travel back to Istanbul and stay in Istanbul.....day 8 leave for US. Days 5, 6, & 7 are too much traveling for a short stay.
I think I'd stay put in Istanbul....and do day trip on the strait, Princes Island, and to the Asian side.