Quick answer

IST is on the European side and SAW is on the Asian side. The best route depends less on the word city center and more on your exact hotel area, landing time, luggage, and comfort with transfers.

Two airports, different decisions

Do not choose an arrival route until you know your hotel area. IST, SAW, Sultanahmet, Beyoglu, Kadikoy, and Bosphorus-side hotels can point to different best choices.

For a first trip, pick the option you will still understand after a long flight. Saving money is useful, but not if it creates a confusing multi-transfer arrival late at night.

Planning Choices

IST
Check metro, shuttle, taxi, or transfer by hotel area. Useful for European-side stays but still far from many areas.
SAW
Often easier for Asian-side stays. Also has metro, shuttle, taxi, and bus options.
Late flight
Favor simpler routes. Especially for first-time visitors and heavy luggage.