...between Christmas and going-home-after-New-Year's), Collins Avenue tended to be a slow-moving molasses-river of traffic, which was OK because we were sight-seeing. The other north-south streets were busy, and even cruising around the side streets was time consuming. We managed to park in a city lot, of which there are a number, though each was rather modest in size; we hit several "dry wells" before finding a spot...and this was with no BCS NC game going on! The whole Miami Beach area is pretty small. A Google parking map is right here.
I seem to recall that they had public transportation, but have no clue where it connects to--probably something goes up and down Collins towards Bal Harbour.