Italy

Are you looking for day-trips from Rome, or are you willing to pay for lodgings elsewhere to extend your range?

Do you plan to have a rental car, or will you be using trains and buses?

What time of year is this trip?

Are you just two adults, or are there also children? If so, what are their ages?

I'm confused. Your other thread says you have 16 days. Have you now increased it to 3 weeks?

As on the other thread, the first thing I would recommend is purchasing a guidebook for Italy. Then READ IT to see what sites, attractions and activities in different cities appeals to you and the rest of your group. Which may differ, depending on whether you are a couple, a family, or some other combination.

Any decent guide book should cover transportation options, but I'd also recommend you look at the Travel Tips section on this site. There is one whole subsection on transportation.

When you mention these other cities, are you seriously asking about doing these as day trips? Off the top, I'd scratch Palermo, since it's over 900 km away. Venice is over 500 km. The others are still a stretch, if you want to see much of anything. Rather than making a base in Rome, consider spending a few days (and nights) in a couple of other cities as well. Venice needs at least 2 nights. Florence deserves at least a couple of days on its own, and makes a good base to day trip to Pisa, Lucca, Siena, and some of the Tuscan hill towns.

If you don't have flights yet, consider a multicity ticket, flying into Venice, then taking the train to Florence. Then train to Rome and fly home from there. If you already have return tickets to Rome, consider flying on to Venice that day, then continue as above.

As CJean said, a good guidebook will have more detail, but there's lots of info right here on this website.

The Travel Tips provide all kinds of links to details about traveling in Europe.

The Explore Europe section has chapters on most European countries including Italy, with details on the cities in them.

My advice is to start with those links, get a good guidebook and do some research. I like Rick's guidebooks for their practical advice. For example someone recently posted about getting fined in Rome for not stamping their bus ticket when they got on the bus. Apparently the guidebook they used told them about getting the tickets but not about the stamping requirement.

Finally, a good way to visualize distances and how long it takes to get to them is by using Rome2rio. You can look at a map, and they provide maps for the various kinds of transportation, but nothing sinks in as well as learning something like it will take 3 hours and 45 minutes to get from Roma Termini to Venezia S. Lucia on the fast train!.

As on the other thread, the first thing I would recommend is
purchasing a guidebook for Italy. Then READ IT to see what sites,
attractions and activities in different cities appeals to you and the
rest of your group. Which may differ, depending on whether you are a
couple, a family, or some other combination.

As a contributor to your other thread, I'll echo this good advance above again. Again, Italy is a big country and you can't day trip all over it from Rome. You really need to get a good guidebook, spend some time with it, and then decide what you are interested in within reasonable reach of Rome if still intending to base there. Palermo, in Sicily, isn't one of those places, and I wouldn't day trip Venice from Rome either. Also, liking "to tour" doesn't tell us anything: you like to tour what? Art? Architecture? Shopping areas? My interests may not be yours.

Very kindly but you haven't given us more to go on than you did with your previous question so responses are going to be pretty much the same.

Although I love Rome and could easily spend 3 weeks JUST there without getting bored, I'd choose more than one base versus try to do all your exploration from there if you want to experience a bit more of Italy. Another thing you might consider is signing up for an escorted tour that arranges the hotels, sightseeing and transport details for you? Have you looked at the RS tours to Italy?

https://www.ricksteves.com/tours/italy

Thank you all for your advice! I get it, get a GUIDE BOOK. Yes, I was vague.

If you are a visual learner, also get a map (there are small ones in guidebooks) to get a feeling about distances between potential sites and what is near them

Along with the good advice for a guide book,to get an idea of day trips from Rome, look here.

https://www.neverendingvoyage.com/day-trips-from-rome/#daytripsfromromemap

It's broken down in time (1,2 hour and longer day trips. Mode of transportation and tours if you'd prefere to not do it on your own. It has a pretty good map.

In addition to guide books, videos can be a great help in learning what places you want to see (or avoid). For Rick's videos, scroll down on this page to Italy: https://www.ricksteves.com/watch-read-listen/video/tv-show

However, the problem is that many wonderful places in Italy are not even a possible day trip from Rome, and others are literally possible but a bad idea. So, are you willing to take an overnight or longer away from Rome?