Perche No! (translated as 'Why Not?') is a wonderful ice cream vendor in the heart of Florence, going since 1939. Not particularly cheap but the ice cream tastes great.
www.percheno.firenze.it/
Via dei Tavolini, 19-red 50122 Florence, Italy
+39(0)55 239 8969
Google map: bit.ly/KldqLW