Floripa, or Florianopils, is a great beach town in South Brazil. I spent 2 weeks there over new year's eve 2006/2007.
My recommendation: you need to rent a car so as to explore the many gorgeous beaches nearby. Try to drive from Floripa to Bal. Camboriu through the coast, you will pass through one beach more beautiful than the other. In Florianopolis alone you will have many beaches to explore which will keep you busy for one month.
But a car is absolutely necessary!
My favourite beach in Florianopolis is PRAIA MOLE, around the Lagoa da Conceicao.
Rgs,
ps: beware: the Argentinians flock to Florianopolis, crowding the city during the summer months. If you want to stay away from them, avoid PRAIA DOS INGLESES!