how much time

No, but keep in mind that Tuscany is a big hunk of terrain that includes Florence.

I'd weight the time in each in this order: Rome, other Tuscany, Florence, Venice.

Rome needs four days, one each in Florence and Venice would suit me fine. I'd also cut a day out of 'other Tuscany' and give it to Umbria instead. Pisa and Livorno are too far out of the way.

Does 10 days include your arrival and departure days? If so you really only have 8.5 days at best (assuming you arrive in the morning otherwise you only have 8 days).

Assuming you only have 8 days and are flying open jaw I think you only have enough time for 3 cities. Rome - 4, Florence - 2, Venice - 2.

If the 10 days does NOT include arrival and departure then I think you should spend those extra 2 days in Siena or San Gimignano and rent a car for one of those days to explore other hill towns.

Most people will tell you that Florence and Venice need more than 1 day. They don't float Ed's boat and that's fine but for a first trip, you should probably give each city at least 2 days.

Rick has a tour that is Rome, Florence and Venice in 10 days and they're experts who know where they're going and aren't relying on public transit (you won't need/want a car for the big cities). As Scott says, if you really only have 8 days, that's just enough time to see the 3 biggies. Rome can easily fill a full week on its own but for just a taste 4/2/2 will work.

Lastly, you will want to fly open jaw--into Venice and out of Rome or vice versa. A round trip flight will force you to backtrack and you'll lose too much time.

Thanks for the advice. I will arrive in Rome in the morning and thought I would spend two nights there, two in Umbria area, two in florence and two in venice and fly home from there.

I would do three location myself. I would rather relax and take in place rather than see as many places as I can