Well off the top of my head you should see
Hagia Sophia
The Blue Mosque (We call it Sultan Ahmet Mosque)
The Basilica Cistern
Süleymaniye Mosque
Topkapi Palace
Dolmabahce Palace
The Bosphorus - Just take a boat ride from Eminonu or Kadikoy
Miniaturk
Kariye Muzesi
Istanbul Archeological Museum
Rahmi Koc Museum
Little Hagia Sophia
Istiklal Caddesi A walk down this avenue will be pretty descriptive in actually how multicultural Turkey used to be
Galata Kulesi
Misir Carsisi This is a must see
Kapali Carsi This is also a must see
These are some of the best eateries in town:
Most any place in Istanbul is child friendly since we like our screaming offspring in tow behind us.
Ciya Kebap
Van Kahvalti Sofrasi - just search for it online and see if you like it
Yanyali Fehmi Lokantasi The English site is a bit bare but a lot of info can be found on them online
Develi Kebap This is sort of fancy but some of the best kebabs in the whole world can be had here, if you feel like drinking a glass of raki or wine with your kebab, this is the place
Beyti Et Lokantasi This is also pretty fancy but it's one of the best restaurants in Turkey if not the best.
Karakoy Gulluoglu This is the best baklava in the world
Haci Bekir This is the place to go for Turkish delights
Short list of kebab places This is a pretty good list, I've eaten in almost all of them, they're really good.
There are two really big malls on the European side of town
Cevahir
Istinye Park
anything can be found in either of these.
If you take a cab from the airport, tell him sternly that you've been to Istanbul before so you don't want the scenic way this time.
I guess this is enough for a couple of days.
There's a dress code for mosques, no shorts and tank tops, just throw a shawl over your head -if you're female-. If you're male and have a big hat on your head, you may want to take it off but it's a ballcap or something inconspicious, don't bother. Don't walk in front of people praying and try not to take pictures of people praying but it's more of a courtesy than a rule. Not making a lot of noise is also customary but no one will say anything if a little child is crying, we're pretty tolerant of children as I said before.
If you come during Ramadan which is in a few weeks, just use your common sense, walking down a busy street outside the touristy areas with a bottle of beer in your hand is bad manners, if you're in the touristy areas, just do what every other tourist is doing, they'll still be eating and drinking. Many muslims also don't fast so don't worry, almost everywhere will still be open.
It can get pretty hot here, especially during noon hours.
Don't forget raingear, it can and does rain with short notice.
If you can spend a bit of money for your comfort, spend it on cab fare. Public transportation is as bad as any big city here.
There's a municipal train line called "Banliyö Treni" in Istanbul.
Do not take it, ever. The other tram lines, subways, ferries etc are good to go.
You can carry a pocket knife. I suggest you do. Pepper spray is also lawful.
I guess this is it.