Four days is the length of trip where Istanbul stops being a checklist of monuments and starts being a city you actually know your way around. The first two days cover the sights every first-time guide points you to. The second two take you across the water to the neighbourhoods that most two-day visitors never see at all.
From Istanbul Airport, the M11 Metro is the fast, cheap way in, or take a direct Havaist bus toward Taksim or Sultanahmet. Buy an Istanbulkart at the airport for around 130 TRY including some credit; it taps for every metro, tram, bus and ferry for the rest of the trip, not just the first two days. Base yourself in Sultanahmet if history is the priority, or Karaköy and Beyoğlu for energy and nightlife.
01
The historic peninsula
MorningHagia Sophia, early, then the Blue Mosque directly across the square. Both are free to enter, though Hagia Sophia's upper gallery now carries a fee for tourists (around 25 euros).
MiddayTopkapi Palace (roughly 40 euros with the Harem) and the atmospheric Basilica Cistern (about 30 euros, buy online to skip the line). Both sit within a fifteen-minute walk of the square.
AfternoonLunch near the Grand Bazaar, then lose an hour in its 4,000 shops. Haggling is expected and part of the experience, not a trap.
SunsetA simit by the Galata Bridge, watching the fishermen work the line as the light goes over the Golden Horn.

If you are visiting three or more paid museums across the trip, the Istanbul Museum Pass (around 105 euros for five days) can save money and time in line. Book Hagia Sophia's gallery, Topkapi and the Basilica Cistern online in advance; peak-season queues are long and the tickets are timed.
02
Water and skyline
MorningA short public ferry from Eminönü up the Bosphorus, a few lira on your Istanbulkart, or a longer sightseeing cruise toward the Black Sea if you want the full run rather than a quick loop.
AfternoonCross to Beyoğlu: ride the nostalgic red tram down İstiklal Street, climb the Galata Tower for the best panorama in the city (around 30 euros), then wander the cafés of Karaköy.
EveningA quick ferry over to Kadıköy for dinner, just enough of a taste of the Asian side to make you want the fuller day tomorrow.

03
Kadıköy and the Asian side
MorningThe ferry from Eminönü or Karaköy, roughly 20 to 25 minutes, timed for the Tuesday or Friday market if your dates line up.
MiddayThe bar and record-shop streets around Kadife Sokak, then a walk south along the water to Moda for the best sunset view of the old city skyline from across the water.
Late afternoonCross back to Üsküdar for the Maiden's Tower view and the İskele Mosque, both far less crowded than their European-side equivalents.

This is also the day to consider the Princes' Islands instead, if a full day trip off the peninsula appeals more than a slower afternoon in Kadıköy. It is a genuinely different day, not an add-on to this one, so pick one rather than trying to rush both.

04
Balat, Fener and the Bosphorus villages
MorningBalat and Fener, Istanbul's most photographed streets and for good reason: colourful Ottoman-era houses on steep lanes, the Bulgarian St. Stephen Church built from cast iron, and considerably fewer tour groups than the historic peninsula.
LunchIn the neighbourhood itself rather than heading back to Sultanahmet for it.

AfternoonUp the European shore to Ortaköy, for its Bosphorus-front mosque and Sunday craft market, and the best spot on this side of the water for a sunset drink with the Bosphorus Bridge lit up behind it.

EveningBebek, a short bus ride further north, the upscale waterfront version of the same neighbourhood feel, worth the extra distance for fewer crowds.
What four days actually costs beyond the sights
Days three and four add mostly transport rather than ticket prices, since neither requires an entrance fee beyond the Maiden's Tower if you go inside (a small additional cost, check current pricing at the ticket office). Ferries between the European and Asian sides run a few lira each on an Istanbulkart, and the bus up to Ortaköy and Bebek is the same. If you swap day three for the Princes' Islands, budget for that day trip's own costs, covered in its own guide.
Four days is enough to stop feeling like a tourist and start feeling like you know the city, without needing a full week to get there. If you only get three, keep day three and treat day four as the one to cut, since Balat and the Bosphorus villages reward a slower pace more than they punish being skipped.