We stayed at the Graceland RV park as well. As others have mentioned felt perfectly safe in the park and Graceland area, but the rest of the area is pretty sketchy.
Take the free shuttle from the Heartbreak Hotel to Sun Records and do the tour, you can then take the shuttle on to Beal Street and do the Stax, Gibson, Peabody etc.. We also did a Mississippi river cruise that really went no where??!! But the announcer/historian was very knowledgable and quite funny.
If you're a baseball fan go and see a Redbirds game. They are the AAA affiliate of the Cardinals and it is great ball with guys trying their hardest to make the Bigs. Cheap tickets and nice downtown Ball Park location.
Forgot to mention we had great food at BB Kings on Beale Street and if your a fried chicken lover ya gotta go to Gus's world Famous chicken down by the river. We did take the Pink caddy from the campground to Marlowe's....