Best place to stay is Lagoa, you'll have everything you need near, plenty of public transportation and have a laid back feel to it.
Florianópolis is a lot safer than other capitals, even on the worst neighborhoods isn't bad compared to Porto Alegre or Curitiba.
Places to avoid at night are pretty much those on the north side of the island and near the city center.
When here invite us for a beer, me and my wife will love to show you the sights