Your hotel is about in the middle of the French Quarter, about the safest part of the city there is. New Orleans knows tourism and conventions pay the bills. If during the week, there may not be too many people out and about, but on weekends there will be plenty. During conventions and such, tons.
You are a block or less from Bourbon Street which is where I assume you will be spending most of your time.
After dark, I wouldn't cross Rampart Street, but there really is no reason for you to go in that direction.
Depending on how many you are, and what you want to do, Tours by Isabelle might interest you, I dunno. I have nothing against Greyline and haven't done either there - just throwing something else out to consider. To the best of my knowledge, Greyline did originate the Katrina tour - the local VP was one of many people who lost his house to the flood.
http://www.toursbyisabelle.com/
A map of your hotel (I know this one says Hotel St Marie) location
and area:
http://www.zydecocruiser.com/nola/pda.jpg