I lived in Memphis for 9 years and lived to tell about it. Be aware of where you are. At night downtown (Beale to hotels) should be fine. Overton Square and Cooper-Young should also be OK at night for walking (within). I have wandered around in the daytime in places I really shouldn't be.
Don't miss the Civil Rights Museum at the Lorraine Motel (even if you're not from the US). Central BBQ has a restaurant nearby if you're hungry then.
A trip to Clarksdale would be great, particularly if its Juke Joint weekend (generally mid April IIRC). Hotels for that weekend are difficult to come by (in Clarksdale).
I was in Columbia MO for the eclipse a couple of days ago. Ate at a restaurant in Jefferson City and the waiter talked about how dangerous Columbia is. My take is generally if you stay in tourist areas and don't get drunk you'll be fine almost anywhere.