Istanbul is a great place to visit!   Nowhere else will you find such a divergence of cultures and such contrasts between the ancient and the modern.  Many women wonder if Istanbul is safe for them to visit as a solo traveler.  Yes, it most definitely is.  Statistically, Istanbul is one of the safest major cities in Europe with a relatively low incidence of violent crime.  Just take the same precautions you'd normally take while on vacation, and you'll be fine, i.e., If you're out and about late at night, take a taxi back to your hotel;  do not wander into dark and deserted streets; do not go off with men you don't know.  If you're a young, attractive female, you'll more than likely attract the attention of the young males of the city.   This attention is harmless, but for some it can be annoying.  The best way to handle any unwanted attention is to remain aloof and make it clear by your demeanor that you are not interested.      

Some bullet points to make your trip  more successful: 

• If you're a female, take a scarf with you when visiting mosques, as most mosques require that you cover your head and not all mosques provide them at the entrance.  
• Wear socks when you visit a mosque, as you'll have to remove your shoes upon entering.  
• If you visit Prince's Islands in the summer, keep in mind that Istanbul residents also flock to the islands during that season.  The islands are also beautiful in the spring and the fall, so don't hesitate to visit during those seasons as well.   
• Bargaining is done mostly in Sultanahmet, and is not common in other areas of the city.  
• When in doubt, ask your hotel staff... they are usually quite helpful and knowledgeable.
• For belly dancing..go to the istanbulin show...its great!
• Must sees on a limited time schedule...Cistern, Blue Mosque, Haghia Sophia, Grand Bazaar, Spice Bazaar, Bosphorous Tour. 

Istanbullus are exceptionally warm, friendly and welcoming, and they're very proud of their city.  They're very eager to converse with visitors, so don't be afraid to enter into conversation with them and don't be taken aback by their friendliness.  You'll get a much better feel for the city if you mingle a bit with the residents, and those interactions may just turn out to be the most memorable part of your trip.   Do, however, be prepared for the onslaught of the many carpet sellers and shop owners who will be trying to entice you into their establishments.  Unless you're an experienced bargainer with an extensive knowledge of the product you're bargaining for, don't expect to walk away with the deal of the century.   If you're not comfortable with bargaining, a simple "no thank you" as  you walk by these shop owners will suffice...provided you keep on walking.  Once you stop to converse with them, chances are you'll soon be seated inside their shop, sipping tea, and closing a deal on a carpet.