Well, if you're coming here as a tourist, it's likely you won't ever venture into those areas (I've lived here for over a year and haven't been into them).
But generally:
Avoid Little Haiti at night and be cautious during the day
Avoid Opa Locka
Avoid LIberty City
Anywhere else is just common sense. Be careful of surroundings. In general (despite all the news stories) it's a pretty safe city. Most crimes the victim knew the attacker.
Anyhow, as to what to do:
South Beach: Do the touristy Ocean Drive, Collins Avenue, LIncoln Drive stuff. Don't eat on Ocean Drive...the food is really bad, but the people watching is great. We'll usually grab a drink at Mangos and hang out for a bit and then head over to Washington/Lincoln Rd. for better food.
If you want more beaches, drive up to Hollywood or Ft. Lauderdale.
The Hard Rock Hotel & Casino in Hollywood has a pretty good nightlife scene and good Vegas style gambling.
THe fun part of Miami is visiting the different neighborhoods. Great food in Coconut Drive or Miracle Mile in the Gables. Go visit Little Havana...have dinner at Versailles (good Cuban food).
There is also the Seaquarium (you can swim with dolphins),VIzcaya Museum, Key Biscayne (if you like outdoorsy stuff).
Feel free to ask....
Oh, good shopping at Aventura Mall (lots of high end stores) and great outlet shopping at Sawgrass Mills.