Hi I am Italian and live in Rome, I have been travelling a lot around the world and agree with people saying that 9 days are not much for all three cities.... however, 9 days would not be many in Rome only either! So I think it is really up to you... I would actually get an italian rail pass, stay 4 days in Rome, travel early by train to Florence (1.5 hr) spend one night in FLorence (two days) and get a night train to Venice (3 days). Or you can get to florence in the evening of the 4th day and spend two nights there.In order to make sure you don't waste your time lining up for museums (Uffizi, Vatican etc), make sure you book the ticket/entrance time in advance. You can do it on the web. You can then use that time to enjoy the atmosphere, the cafes' and strolling around! You will definitely see a lot, enjoy it, and think you want to come back to see more! Have fun!