8 days is not a lot of time but is doable to have a great vacation. Personally. Rome Florence and Venice are my 3 must (nothing bad to say about Naples, or Milan or Turin,...)
Rome might require 3days easy to have a good look around. Stick with Rome cuz it s more than enough. Def Vatican and Musei Vaicani + colosseum and Fontana di Trevi, Piazza di Spagna, Piazza Navona....Can be done in 3 days good.
2 days in Florence again enough, but you might want to go see Pisa or Siena for a day, which are great.
Venice can be done in 2 days if you hurry! lol but i d recommend 3, go to Burano and Murano Islands as well.

Might be really cold dou!

If you go to three cities you won't have eight full days, unless you get from one to the other by magic carpet.

To elaborate on trains - cars are useless in cities like those and tourists' cars are banned from large parts of them - so take trains - www.trenitalia.com and www.italotreno.com are two competing rail companies using same tracks and stations - check both for lowest fares and booking well in advance to get limited discounted tickets can save a ton over waiting until there. www.seat61.com has adroit advice on booking your own online discounted tickets; for general info on trains www.budgeteuropetravel.com and www.ricksteves.com.

Day trips are easy by bus or train but with 8 days and as bvlenci says with travel between that makes really six days for three cities you may not have time for many. Siena or Pisa from Florence are easy to see an iconic Tuscan hilltown or the Leaning Tower.

Thank you all for your help!

<The town of Bracciano itself has little to recommend it, but the castle, on a hill overlooking the lake, is worth a visit. Tom Cruise and Katie Holmes got married there.>

An easy and great day trip from Rome I took - combined it with a daytrip to Viterbo.