If Miami, and not Miami Beach, then I recommend Coconut Grove. If you're willing to go farther and if you're a sassy shopper, then I recommend Sunset Place, West Palm Beach's CityPlace, and Las Olas Blvd (romantic but expensive) in Ft. Lauderdale. If you like malls, I recommend Dolphin Mall in the western part of the city or Dadeland in the southwest (you can take a MetroRail to Dadeland although you might have to walk at least a block to get to the mall). For a really upscale "pretty" mall, I recommend Village at Merrick Park in Coral Gables. For cheap but good late night pizza inside Miami, I recommend Casola's just north of US1 on SW 17 Ave. It all depends on what you're looking for.
And for the view of Miami, you can't go wrong with taking the metromover around Miami (it's like an airport tram, but some tram stinks). But the view is nice and it's a free ride. From the metromover you can also easily go see Miami's downtown library, art museum, bayside marketplace (mall by the ocean), and there's plenty of dining options in downtown.
If you don't have a car, avoid Miami at night, just to be safe (although it is not dangerous, but it's always better to be in the company of people - for this reason, people recommend you to be in Miami Beach at night if you plan to go out at all, without a car).