Yes, there is a very nice Jazz Club in Via de Caccini, Borgo Pinti Corner and several good rock venues like Viper Theater and Flog..here you are the links:
Yes, you should also try Be Bop in Via dei Servi (a lot of live music): www.bebopclub.com and Unplugged of Via dei Saponai 14/r....
Enjoy and let us know... Would you like to write an article about live music in FLorence? We'll publish it with your name in studentsVille.it and in I-Florence.com !!!