Zurich to Cinque Terre

Looking at Rome2rio.com looks like you can do it by train, but takes about 9 hours and involves several train changes.

Easy by train, Zurich to Milan, Milan to Genoa, then local train that serves all 5 villages. A long day of traveling or you could break the journey in Milan.

The DB schedule website shows, for departure from Zürich before noon, that there are currently multiple 7½ hr connections to Vernazza with changes in Lugano, Milan, and Genoa or La Spezia. La Spezia and Vernazza are on either end of a regional train line that goes along the coast connecting the towns of the Cinque Terre.

You can take a look at the schedule on the Deutsche Bahn website.

If you don't yet know what town you'd like to stay in, just use Monterosso for the schedule look-up. Times and frequencies may vary by day of week, so if you know what day of the week you'd be making the trip, use a matching date in the immediate future.

There are actually direct IC trains from Milano Centrale to Monterosso, the largest of the Cinque Terre villages, about every 2 hours starting at 6 am (but no 10 am train). Frequent local trains from there to the other four villages.

There are also direct trains from Zurich Hbf to Milano Centrale every 2 hours. By July next year, should be even faster than shown today when the new Ceneri Base Tunnel opens.

What I don't know is whether scenery along the way would justify taking something other than the fastest route--especially after that tunnel opens. There's not much scenery in tunnels.

But if there is a 10-day rail trip through the Alps before that, maybe you will have had your fill of gorgeous scenery. Seen one Alp, you seen 'em all. :-)

Thanks for the great responses. Would we be better off taking a train to Milan and then getting a car and driving to Vernazza etc?

A car is not advised in the CT. The towns are car free, with the exception of Monterosso. Take the train.

Would we be better off taking a train to Milan and then getting a car

What do you mean by "better off"? Time-wise? Cost-wise? Comfort-wise? Convenience-wise?

Time wise: according to ViaMichelin, the time to drive to Vernazza would be 3H05. German Rail shows a few connections from Milan to Vernazza at 3H18, others in between 4H08-4H13. So if you used the 3H18 trains, you would save very little in time, and undoubtedly spend more than the time saved getting the car. Even using the 4 hour connections, you might not save any time considering the time to get and return the car.

Cost-wise: again, per ViaMichelin, the cost of fuel and tolls from Milan to Vernazza is about €38, and that doesn't include the rental cost of the car. And you probably can't return the car in the Cinque Terre, so you would have to pay rent for the car (not to mention parking fees) to just sit for days.

Comfort-wise: Would you rather be confined to sit in a car seat for 3-4 hours vs a larger train seat and the opportunity to get up and walk around?

Convenience-wise: As someone already said, the towns of the Cinque Terre are traffic free. You would have to park outside, probably farther away from the town than the rail station.

We parked in Monterosso in a large lot near the waterfront. But we left it there for three days. It was convenient to have it to get there from the Italian lakes and then to drive on to next stop in Tuscany. .

As others have said, you do not want or need a car in the Cinque Terre. It would be parked during your stay there, gathering dust and incurring parking charges. A car also comes with a few additional issues. Each driver listed on the rental form must have the compulsory International Driver's Permit, which is used in conjunction with your home license. You'd also have to be very vigilant to avoid the ZTL (limited traffic) zones which exist in many Italian towns (hefty fines for each pass through these).

There are extensive rail connections in that area so you won't have any trouble with transportation. However it will be a longer journey from Zürich. The travel time and train choices will depend on what time you want to depart Zürich. On the current schedules, there's a departure from Zürich main station at 12:10, arriving Monterosso at 19:05 (time 6H:55M, two changes at Arth-Goldau and Milano Centrale). Of course the schedules could change slightly by July 2021.

The travel time will vary slightly depending on which of the five towns you want to stay in. Monterosso will provide the quickest time as it's the most northerly town and the first one that trains from Milan reach. I normally stay in Monterosso as it's the largest of the five, and therefore has the best selection of hotels and other tourist amenities.

Thank you to everyone who has giving me ideas. We are now considering a train from Zürich to Milan staying in Milan several days and then instead of heading to Monterosso we thought about going to Santa Margherita Ligure and then taking the ferry to Vernazza and staying a few nights there. That way we could see Portofino and the rest of Cinque Terre. We will have five days so any thoughts from anyone who has done this would be highly appreciated!
Thanks

One thing to be aware of is that in there are big changes in the Switzerland - Italy timetable planned for next year. The opening of the Ceneri tunnel means shorter travel times to Milan, and SBB is planning on running more trains to destinations beyond Milan. One of those is direct train to Genoa, which can be handy for getting to the Cinque Terre.
Departure is going to be 8:33, arrival Genoa 13:49. There you could then change for a local to any station along the coast further south.

That train is showing up on the schedule, at least the date I checked on February 10, 2021. It saves even more time by skipping Milano Centale, a "dead end" station, and stopping at through stations at Milano Lambrate and Milano Rogoredo. 5 1/4 hours from Zurich Hbf to Genova Piazza Principe. Frequent trains from there to Santa Margherita Liguria.