I live in Elephant & Castle (recently moved from Walworth 5 mins away) and though its not the best area to live in I haven't heard any gun shots, seen any dead bodies or such so don't be scared by silly people telling you its a ghetto or such.
I'd say the "best" place close to Elephant & Castle is Kennington, there's a big park (kennington park) and the Northern line goes straight through the district.
Kennington is literally 1 minute from Elephant & Castle.
Neighbouring Walworth is ok in parts and is the cheapest area in inner London so check that out. Many students seem to live in the area recently.
I'd say Walworth is a bit more down market from Kennington.