Count me as one that says skip Venice, especially if you only have 1 day for it. By the time you get to Venice, take the boat to the vicinity of the hotel, find the hotel, check in, etc. you'll only have a few hours left anyway during the day. At nite not a lot to do; wandering around the streets is nice, but that's about it. I am one of those people that isn't blown away by Venice, though. Thought it was crowded, expensive, and just not as delightful as other places I've been in Italy.
As for Rome, there's so much to see I don't think you can exhaust it in 3 days or 3 weeks; however 2 nites is fine for a first visit and you can always see more another time. One trap people fall into is trying to see everything; intead pick a few things you want to see and take the time to enjoy them. I'd highly recommend a walking tour of the Colosseum and Palatine area with any of the guides Rick recommends; also the twilight tour of Rome was a favorite. Those tours, a few other sites you pick from a guide book you want to see (or just time spent wandering around), you'll have a great time.
A car is worth renting in the Tuscan area; you can get to many by train (then bus up the hill) but a car gives you much greater convenience and you can visit those not as easily reached by train.
I'm a fan of the Cinque Terra; when its sunny it is stunning! I'd spend 3 nites so you have time to hike, walk around, and just relax at the beach (drop a day if you're not a relax on the sand person).
Lastly, since yuo're spending 10 days or so in italy, its worth your time to learn a few phrases, numbers, etc. Your local library probably has the pimsleur series. Do at least the 1st 15 lessons (30 min each) and you'll know a touch of italian, but it really makes a difference!