Venice is certainly expensive and crowded. So are the other cities, though Venice is perhaps more so, given its size and its unique topography.
It may be more a reflection of my interests but there aren't as many day trip destinations in Rome and Venice as there are in Florence. I'm talking about places that could be reached within 2 hours drive or bus or train ride each way.
Viator's is another good site, which offers different kinds of tours. Some are better values than others but they also give you an indication of what the tourist operators in a given destination offers, especially in the way of day trips and what they offer is also an indication of the popular attractions. Of course some people may specifically want to avoid the beaten path.
I've been to Rome many times, because it's often a transit point through the rest of Italy, so I usually end up staying at least a night or two before flying back to the US. So I've seen the major museums at least a couple of times, though I'm not as enthusiastic about spending the better part of a day or even an afternoon in a museum as I used to be. Certainly worth seeing at least once, though with the crazy crowds (literally queues around the block for the Vatican Museums), it might be worth buying guided tours, which get you into the museum through much shorter group tour queues.
But since I'm doing more photography, I've gravitated more towards exterior attractions (hassle to get into some museums with gear, even if they let you photograph inside) or open air museums like the Roman Forum.
It's hard to conceive of spending a week (7 full days, not counting the arrival day) in Rome unless taking time to go through the major museums and attractions, like one a day. The Forum is an afternoon, the Colisseum is maybe half a day (more like a couple of hours or skip altogether as there are better preserved colisseums in Europe, though not as big and famous). Vatican Museums and Sistine Chapel and St. Peter's Square is 1/2 to a full day, depending on how much you want to digest the art and going through the galleries.
Main day trips are Villa Este/Hadrian's Villa and Ostia Antica. Some people will spend long days, well over 10 hours, to go to southern Tuscany or Umbria, like Orvieto or Assisi. Or some will try to get to Pompeii from Rome, which is a real long slog.
8 Great Day Trips from Rome – Touropia Travel Experts
One of two of those marathon tours could allow for an extended stay in Rome but I went to Sorrento and the Amalfi Coast to visit Pompeii as well as other attractions down there. Or for Tuscany and Umbria, it was renting a car and basing around Southern Tuscany, say Siena or towns to the south of it. Even then, kind of long drives.