If you look at a map of S Miami:
http://www.cityofsouthmiami.net/clie...ut/CSM_Map.gif
you'll notice it's kind of an L shape.
The part south and east of US 1 are basically indistinguishable from Coral Gables, very nice and very safe. In fact, in some areas, the only way to tell if you're in S Miami vs C Gables is by looking for the low, white, concrete street name markers that C Gables uses.
Downtown S Miami is a nice,
almost charming little area; very safe to stroll, shop or just get a coffee or cocktail. Some of our favorite restaurants are there.
The chunk just north & west of US1, closest to downtown, is the worst part imo.
JacobMax said it perfect:
"The area west of US-1 and Red Rd, north of Sunset Dr, east of Ludlam Rd and south of Miller Rd is a little old ghetto, is not that dangerous, but it is very unsafe."
Personally, I would drive through there at night, but I wouldn't jog through there during the day.
As you head west and north, it gets better again. Perfectly fine and safe, just not AS nice as south of US1.
As to the "safest" parts of Miami, imo, I think it's more about what you can afford and want out of an area.
Already mentioned, Doral, Kendall, most of S Miami or Coconut Grove, all of Brickell, Key Biscayne, Pinecrest or C Gables are about as safe as Miami gets. Most of Miami Beach, Aventura ...
I think you're better off working backwards. Which neighborhoods are you looking at and are THEY "unsafe." The "rougher," less safe areas are
usually pretty obvious if you're on the ground looking at places, but not always.
Good luck.