I spent 20 days in Italy this past summer. I'm one of those tourists who enjoys himself anywhere he goes, so I don't have much bad to say about anyplace. But I'll try to give you the good and bad about each place.
I'd advise four full days for Rome.
The good: For me the Colosseum and Vatican and food were the highlights. I also enjoyed Sunday in the Villa Borghese. Best pizza was at Pizzarium and best gelato came from Fatamorgane -- both on the north side of Vatican City. The Roma Pass was useful for reduced admissions, avoiding long lines at the Colosseum, and using the subway.
The bad: The Forum and Spanish Steps were a bit disappointing. A lot of the tourist areas are overrun with street hawkers from Bangladesh and Africa, and this may deviate from your perception of the Rome of your dreams. Hotels are expensive here.
I took three days for the Campania area: one for Naples; one for Pompeii; and one for the Amalfi Coast.
The good: I was apprehensive about Naples because of it's reputation for grit and unsavory characters, but I was glad I spent a day there. The National Archaeology Museum has one of the world's great sculpture collections. The town seems to get a bit better as one moves away from the train station. I'm not a shopper, but some women who are shoppers advised me that if you want to buy something in Italy, buy it in Naples: it's cheaper. And this seemed true. Pompeii is a much more impressive ruin than the Roman Forum and gives a better idea of everyday life at that time. I advise staying in pretty Sorrento rather than gritty Naples and spending some time to explore the Amalfi Coast. The best gelato I had in Italy came from Raki's in Sorrento. If you're a hiker, walk the Path of the Gods from above Amalfi to Positano. The Unico Campania card lets you ride trains and buses in the area and the Naples subway system.
The bad: Naples is rather unattractive around the train station. Beware of pickpockets and other ripoff artists: you'll notice the same oily people working the trains and stations, especially between Naples and Pompeii. Although the transportation system isn't bad, you'll need to allow time to move between Naples, Pompeii, Sorrento, and Amalfi -- and travel light because there isn't much space for luggage. Even though Sorrento, Positano, and Amalfi are considered seaside resorts, you won't find much in the way of beaches there.
Three days will give you a good enough dose of Venice.
The good: Some places call themselves the Venice of the North, the Venice of America, the Venice of Asia, but there's really no place like Venice in the world. It really hasn't changed much in appearance from the old cityscape paintings you'll see in the museums. I loved walking around. (It was easier than I imagined because of frequent signage pointing to the major sites.) The city and waterways were cleaner than I anticipated. Fresh fruit from the Rialto market tasted great.
The bad: It's expensive, especially the hotels and the transportation, though a vaporetto pass eases the cost some. Moving with luggage is a hassle here. In Venice, I always had the sense that I was in a living museum rather than a real, contemporary city. As such, the amount of tourism might get to you (even as you contribute to it). Venice offers much in the way of the art and history and novelty, but outside of those elements, the city is pretty limited. Not a lot of nightlife here, especially gay nightlife. (You have to travel to mainland Mestre for that.) Overall, outside of Milan, the gay nightlife in Italy was disappointing. Too much Catholic repression. But you've got Amsterdam for that.
So then spend four days in Amsterdam. I haven't been in over 20 years, but I'll always remember it as city in Europe where I had the most fun. I like the Dutch people a lot. Outside of the Indonesian restaurants, the food's not great, but the beer is. Enjoy the beer, the museums, and the Dutch men!