We are a family of 3 with 2 days in Florence, 3 days roaming Tuscany, and 2 days in Rome in May 2013. I am not anticipating that my husband and son will last long visiting museums and churches, or even shopping. Both like gardening and gardens, though. Other than the obvious Florence choices (e.g. Boboli) and the impossible Tivoli, what are some gardens we can visit?
In Florence, besides Boboli, I recommend the Giardino dell'Orticultura, and also the Giardino dei Semplici. Near Piazzale Michelangelo there are several, including Bobolino, the garden of Roses etc. This is a comprehensive list of gardens in Florence: http://it.wikipedia.org/wiki/Giardini_di_Firenze Rome has a lot too. Villa Borghese is probably top, however if you have time for more they have the Bioparco, Orto Botanico, Pincio, Gianicolo, Villa Pamphili and dozens and dozens more. This is the City list: http://www.romaspqr.it/roma/Ville_e_giardini.htm
A unique site in Rome is Villa Torlonia. Beautiful park for strolling, interesting and historic buildings to visit. Please note that gardens here are not floral like in many other places, although there is a nice Rose Garden at the base of the Aventine.