As a St. Jude patient, I've been going back and forth to Memphis since 1980. I've seen highs and lows of the City but I've never had any personal issues but that doesn't mean anything really...
I've stayed in the worst hotel (Downtowner 1980) and I've stayed in nice ones too Peabody, Sheraton, Crowne Plaza, etc. I've walked by myself all over downtown (during the day), Beale Street, and alleys to get to Rendezous, etc. and always felt safe. Hollywood was scarier to me than Memphis....but Hollywood is a bit freaky.
That's not to say that you don't need to be cautious. Memphis is the only place where I've been to a mall and each store had their own security guard. St. Jude Hospital even cautions their families about the dangers of the city...so there definitely things that need to be taken into consideration when you're out and about.
I've always been told to stay out of West Memphis (however this has improved over the last few years), and the area around the airport (I've driven through this area and it has many abandoned buildings). I never visited Liberty Land because my parents had been told not to take us there....I wish they would have though.
The Bass Pro-Shop was very nice, so I'm sure that the Mud Island revamp would be very welcome and continue to greatly improve that area of the City.
Jay