Quick answer: Five days lets you cover Sultanahmet’s icons, the bazaars, the Bosphorus, modern Beyoğlu and the Asian side.
Five days is generous for Istanbul, with time for both the headline sights and the city’s everyday rhythm.
The itinerary, day by day
Day 1 — Sultanahmet
Hagia Sophia, the Blue Mosque, the Hippodrome and the Basilica Cistern.
Day 2 — Palaces & bazaars
Topkapı Palace, the Grand Bazaar, the Spice Bazaar and the Süleymaniye Mosque.
Day 3 — The Bosphorus
A Bosphorus cruise, Dolmabahçe Palace and the waterfront at Ortaköy.
Day 4 — Beyoğlu
İstiklal Street, the Galata Tower and Karaköy, with a meyhane (tavern) dinner in the evening.
Day 5 — The Asian side
Cross to Kadıköy and Üsküdar for markets and the best-value food, or take a Princes’ Islands day trip.
Where to stay & when to go
Base in Sultanahmet for the sights or Beyoğlu/Galata for a livelier feel. Get an Istanbulkart for transit. Spring and autumn are most comfortable.