Little Havana (mostly 8th street, Calle Ocho)- you have LGC, Pepin, and some small family run places. Get a cuban coffee at any corner place, and smoke out on the street with your coffee. On Flagler there is Padron. Check out La Carreta or Versailles or any little cafe for good Cuban food. Check out the domino park and the Bay of Pigs memorial while you're on 8th street. All of it is walking distance and a great way to kill a morning/afternoon. Get out by dark, just to be safe.
As far as S.B goes, check out Lincoln road. Lots of shops and bars with a great jazz club. Otherwise, SB is expensive so plan on dropping coin if you go to the clubs.
Downtown Miami has Bayside, an outdoor shopping mall with some cool stuff, Hard Rock cafe, Hooters, etc.
If you have a car, drive to Key Largo, about an hour south of Downtown.