If you are the partying type than Bourbon Street with all of it's bars and clubs will appeal to you. My wife and I don't enjoy that but we have found a lot to do in New Orleans.
The french quarter, the garden district, riding the St.Charles Street streetcar and enjoying the great food are at the top of our list. We have taken several walking tours and really enjoyed them. Check out activities on Trip Adviser and decide what looks like fun.
As long as you are street smart and watch were you are late at night, crime should not be an issue. It is a unique city!