Denise, I really don't think you need to worry. Use common sense just as you would at home and you will be fine.
I've been there 4 times in the past two years and I walk everywhere, often alone, at all hours of the day and night. I've never had the least concern or trouble.
Keep your valuables locked in a safe or in the hotel safe and then you needn't be concerned about that either. This is a standard precaution taken by most travelers no matter where they go.
[This message has been edited by seashell (edited 04-24-2002).]