Istanbul is the European city where the neighborhood pick changes the most. Sultanahmet is what shows up in searches; it's rarely the right answer beyond night one.
Sultanahmet — first night, sights only
Sultanahmet has every imperial sight at the door — Hagia Sophia, Blue Mosque, Topkapi, Basilica Cistern. By 4pm the day-trippers leave and it goes quiet. The restaurants are tourist-priced; the streets feel themed. Best for: 1-2 nights, sights-focused first-timers.
Beyoğlu / Galata — the locals' Istanbul
Beyoğlu (Galata + Karaköy) is across the Golden Horn — the Galata Tower, İstiklal Avenue, the design hotels, the cocktail bars. Where most travel-savvy visitors actually base. Walkable to Sultanahmet via the Galata Bridge in 20 min. Best for: stays of 3+ nights, food-focused trips, return visitors.
Kadıköy — across the Bosphorus
Kadıköy is the Asian-side residential-and-market quarter. Moda is leafy, fish markets, the densest local food in the city. Daily ferry to the European side. Best for: longer stays, food-focused trips, anyone wanting real local life.
Beşiktaş — Bosphorus residential
Beşiktaş is north along the Bosphorus — football quarter, Dolmabahçe Palace nearby, ferries up the strait leave from here. Cheaper than Beyoğlu, less iconic. Best for: budget-conscious trips, return visits, anyone whose trip is up-the-Bosphorus focused.
The honest itinerary
For a 5-night first trip: 1 night Sultanahmet (so you wake up to Hagia Sophia at 6am), then move to Galata for 4 nights. The two-base approach beats any single neighborhood.
Compare: Sultanahmet vs Galata, Galata vs Kadıköy, Sultanahmet vs Beşiktaş.