Cinque Terre is absolutely stunning - although quite small. There's a trail that connects all five villages which is a great thing to do, but I wouldn't plan on spending more than two days there.
As for Rome, it gets mixed reviews. If you're really into history, then it's incredible. I've done five-six days in Rome and was more than satisfied. However, a group of six who likes hiking... I wouldn't spend more than a couple of days.
Florence and Venice are incredible, but more importantly, the greater wine region of Tuscany is not something to overlook. If I was going with five other friends... I'd be spending as much time as possible staying in Florence and Venice and doing daily trips out to the wine regions.
Milan is extremely overrated in my opinion - would steer clear of that.
Maybe consider... Rome to Cinque Terres, Cinque Terres to Florence, Florence to Venice, Venice back to Rome?
Florence!! Easy to do in a few days. Great food, wine, and people. Make sure you stay across the Arno away from all the tourist destinations. You can easily walk to anywhere you want to visit, but the best local food and wine is across the river. I recommend Piazza Santo Spirito and any restaurant in it.
Whenever I have friends or family visit Rome, I always, always recommend my favorite gelato stop! Just a block and a half from the Pantheon: Giolitti. They have more flavors of gelato than any other place in the city, and they're delicious and affordable! We went more times than I can count, and I never ran out of new flavors to try!
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You'll love Cinque Terre. A must-see location nearby is Lucca. I'd skip Pisa and stay 2 nights in Lucca - spend one morning riding bikes along the top of the wall (you can rent them in multiple locations, or pick a hotel that provides bikes at your disposal) and spend the afternoon walking the city. You can easily make Cinque Terre a day trip from Lucca and spend a whole day there. We stayed at La Boheme: http://www.boheme.it
In Tuscany, I'd recommend Sienaas your base of operations for 3-4 nights and drive to several hilltops villages during that time: San Gimignano, Greve In Chianti, Montepulciano or Arezzo are all lovely, but you can't go wrong anywhere in that area. If you're foodies, the town of Panzano in Chianti has a famous butcher shop with a celebrity butcher (I can't remember his name now, but that was kind of fun). We stayed at Hotel Palazzo Ravizza: http://www.palazzoravizza.it/en/
Consider a cooking school or even just one day of cooking - there are a number of places in Tuscany and Umbria that can accommodate a group your size. We took a walking wine tour through Siena that was wonderful: http://www.tuscanwineschool.com
Have fun - it'll be a trip you'll never forget!
10 days is not a long time. I think all the other suggestions are great -- all of Italy is quite beautiful. But if you really want to enjoy the city and the coast, then the only thing I'd add - don't try too see it all and do it all.Since your priorities are Rome and the Italian Riviera you know where to start. Allow yourself at least two days, preferable three for Romeand at least the same for Cinque Terre and the surrounding area, and then I'd pick one more area - a great option would be Tuscany, focusing on Sienna and Florence, with some trekking (horseback riding and/or cycling) in wine country. (I love the Amalfi Coast, but you'll lose a lot of time on the road). Take your time, talk to the people and enjoy the food and wine. You'll have a great time.
I went to Italy last summer for 9 days last year. I went to Venice, Florence and Rome for 3 days each and I would highly recommend that length of time in each place. Florence was the favourite of all locations mainly due to it being incredibly picturesque and surprisingly quiet for the time of year.
Ciao, I will recoomend to saty in the Cinque Terre area for at least 3 days, for the accommodation and other info. you can visit www.cinqueterreonline.com ciao
I'm Francesco from Rome and I can suggest you to make a visit in my city in this way: first day you can make a tour in bike to see the most important places of Rome, second day you can visit the Colosseum and the roman forum (booking online you can skip the line): http://www.coopculture.it/en/colosseo-e-shop.cfm
in the thind day you can visit the Vatican and Vatican museum http://biglietteriamusei.vatican.va/musei/tickets/do?weblang=en&do
In the four day I suggest you to visit the Appian way Via Appia Antica, renting a bicycle or a scooter.
Other places in wich you can have a really good pizza are DAR POETA (vicolo del Bologna, TRASTEVERE) and LA MUCCA BISCHERA Via Degli Equi, near Termini station, and PIZZERIA REMO Piazza di Santa Maria Liberatrice TESTACCIO.
Can you give us a little more information? When are your flights and where do you fly into and out of?