Istanbul is excellent value compared to Western European capitals. Budget travelers can manage $35-55/day: guesthouses in Sultanahmet run $20-35, a doner or lahmacun from a local place costs $2-4, and public transport (Istanbulkart) is very cheap. The ferry system connecting European and Asian sides costs about $0.60.
Mid-range travelers ($80-130/day) can stay in boutique hotels in Beyoglu, eat at proper meyhanes, and visit all major sights. Museum entry fees are reasonable ($5-15). The Istanbul Museum Pass covers major state museums and saves significant money if you're visiting several in a short period.