Istanbul's tourist areas are well-traveled and generally safe. The Sultanahmet, Beyoglu, Besiktas, and Kadikoy areas see millions of visitors annually without major incidents. Standard big-city caution applies: watch for pickpockets in the Grand Bazaar and crowded Istiklal Street.
Taxi scams are common: always insist on the meter running, or use BiTaksi or Uber (available in Istanbul). The 'shoe polish scam' — a man drops his brush and asks you to pick it up, then insists on polishing your shoes and demands payment — is widespread near tourist sites. Simply decline and keep walking. Check current travel advisories before visiting border areas.