Quick answer: Istanbul runs about EUR 65 per day mid-range - noticeably less if you eat local and walk. Cheapest window: April–May or September–October.
What things actually cost
simit from a street cart
0.50 EUR
glass of cay
0.60 EUR
doner durum
3 EUR
tram ride with Istanbulkart
0.70 EUR
ferry across the Bosphorus
0.80 EUR
Turkish breakfast spread
9 EUR
Eat well for little
Balik ekmek by the Galata Bridge - grilled fish sandwich off the boats, about 3-4 EUR
Ocakbasi kebab at Zubeyir in Beyoglu - charcoal-grilled skewers at the counter, about 15-20 EUR per person
Meyhane night on Nevizade or in Kadikoy - a spread of meze with raki, about 20-25 EUR per person
Turkish breakfast (kahvalti) in Cihangir or Kadikoy - a table full of cheeses, olives, eggs and honey for 8-12 EUR
Kunefe for dessert - hot cheese-filled pastry in syrup, about 4-5 EUR
Money mistakes to avoid
Never leaving Sultanahmet - the real city is in Beyoglu, Besiktas and Kadikoy; cross the water at least once
Falling for the dropped shoeshine brush or a friendly stranger's bar invitation - both are classic setups, walk on
Taking street taxis without the meter - insist on the meter or use the BiTaksi app instead
Paying per ride in cash - get an Istanbulkart immediately; it roughly halves every tram, metro and ferry fare
Transport without the tourist tax
From Istanbul Airport take the Havaist bus or M11 metro to the center (4-6 EUR, 60-90 minutes). In town get an Istanbulkart (a few EUR plus top-up) and use trams, metro and the commuter ferries, with most rides costing under 1 EUR - the Bosphorus ferry crossing is the best 1 EUR in the city.