Rhine Falls

There's a train to Schaffhausen. It takes about an hour. A cab would be faster and take you right to the falls, but considerably more expensive. I've only driven there so I can't say what it's like to get from the train station to the falls, but there should be local transport.

Be advised you will want to have rain gear and good, waterproof shoes. Not only has the weather been cool and rainy, but the falls generate a lot of air-born water, especially if you take a boat ride.

It is very easy to reach the Rhine Falls from Zurich.
You can find the connections at https://www.sbb.ch/en

There is a train line on both sides of the Reinfall. The stop on the western bank is called “Neuhausen Rheinfall”, the stop on the eastern bank is called “Schloss Laufen am Rheinfall”. There is a boat to change banks below the falls.
It's a 50 minutes train ride from Zurich.

If we were not to take the boat which side would you recommend?

I rather like the Swiss side, but both are good. The train on the German side pops in and out of Germany and Switzerland many times in a very short distance.

I call it the German or Swiss side because of the country near to the side of the river and falls, but I think that the entire falls is within Switzerland. The border there can be described many ways - a straight line is NOT one of those ways.

point of trivia - the Youth Hostel in Schaffhausen is/was a really nice one. I spent nearly a week there in 1972, but my most recent visit to the Falls is much more recent.

https://community.ricksteves.com/travel-forum/switzerland/interesting-town-near-swiss-german-border

Get off at the Neuhausen Rheinfall stop. Short walk to the falls and there is also an elevator if you need it. Very simple trip.