Italian trains

Welcome
Most all trains run on Sunday

Train travel in Iraly
https://www.seat61.com/train-travel-in-italy.htm

Official train site
Trenitalia-fast trains and regional
https://www.trenitalia.com/en.html
Use Italian station names

Private company-fast trains on select routes
ItaloTreno
https://www.italotreno.com/en

Both have easy to use apps

Ginger,

Where are you planning to travel in Italy?

Some smaller towns are reachable by bus so be aware that bus schedules are limited, or nonexistent, on Sundays.

Check bus schedules in advance of your trip.

Enjoy your time in beautiful Italy!

Trains run every day, including Sundays and holidays, and pretty much with similar frequency.
Buses, not so much. So if you plan day trips by bus, to locations not served by rail. you are better off if you travel on weekdays.

Hello ginger12franz, and welcome to the forum,

When are you traveling? You can check the current Sunday and weekday schedules now for routes you are interested in because they don't change that much. Height of summer versus dead of winter may have different frequencies and you can't count on an exact time but if there are 10 trains on a Sunday in October you can count on about that many in April for example.

There are two fast train companies:
Trenitalia - the state run company that also runs local trains - https://www.trenitalia.com/en.html
.Italo - that only runs fast trains on popular routes - https://www.italotreno.com/en

Fast train tickets can be bought in advance trading lower price for decreased flexibility and local train tickets regionale don't need to be purchased until you need them.

Rome2Rio.com is not a reliable site for serious planning but it is any easy way to sanity check how long it might take take to get from A to B and get an idea of the options.

Happy planning,
=Tod

Some local train lines that cater mainly to workers and student (FAL south from Bari comes to my mind) may have bus service only on Sunday, and somewhat sparse. But as a general rule, trains run on Sunday and festivities on their festive schedule.

Thanks so much! I want to travel from Naples to Monterosso al Mare,( or one of the Cinque Terre towns), then a few days later go on to Venice. Thanks for your help!

You can search for La Spezia to check schedules for CT since it is the largest local station and you can get trains to any of the towns from there. The same train that goes to La Spezia may well stop in a specific CT town but using La Spezia is easier for scheduling even if you don't use it. This will realistically probably take you 4+ hours from Milan.

Another point is that going from CT to Venice is connecting two places with difficult infrastructure and crossing Italy at nearly its widest point. That means you will probably need to dedicate an entire day - 7-8+ hours door to door - to make this happen.
I would encourage you to get a proper idea of the travel times before setting your schedule in stone.

Have a great trip,
=Tod

Naples to La Spezia will take about 6 hours-change in Rome

With train travel you can plan trips end-to-end between any two stations basically.

So you do not need to plan different segments separately. Just go to www.trenitalia.it and look up train times and prices from Napoli to wherever it is that you plan on basing yourself in the CT.
Monterosso is a good base btw, because it has IC services.

Oops, I misread OPs second post and posted times for Milan instead of Naples. Naples is even further so you are committing to spending nearly two full days - 6+ and 7-8+ hours - engaged in travel on your current itinerary. Only you can decide if you'll have enough time in those places to make the trade off of those days worth the time spent getting there.

Part of planning is getting all the information and making choices - sometimes hard choices - about what you have time for and what you'll most enjoy. All I can say if make sure you're spending enough time in those places that your memories are of Italian cities and people and not just Italian trains and travel logistics.

Whatever you decide have a great trip!
=Tod

Good advice! I will look at some other options to maximize our time in the places we really want to see. Thanks for your help. This group is wonderful-it is good to know there is a place I can go to for information I can trust!
Ginger