I've never had cause to visit Beringen but I've been to Schaffhausen several times over the years, most recently 3 or 4 years ago.
I like that part of the world (by the way I think Google maps has it wrong - there is a "c" in the name), but be aware that it is not as impressive as, say Niagara Falls. But you can ride a boat, or walk up to the falls and it is rather fun.
The German/Swiss border is very convoluted in that area, and going on some roads you go in and out several times. Beringen is actually north of Germany.
My first experience there was in 1972 when I stayed in a really nice (comfy, scenic, good kitchen, clean facilities) hostel.
In recent years I found that parking wasn't too bad, later in the day. A short walk down to the river, or across the river.
The boats weren't fabulous but were fun. I very much enjoy walking in and around the river and the falls, there are parks adjacent to the falls, at least on one side. I haven't explored the other side very much.
If coming by train to the falls you are better getting off at Neuhausen rather than at Schaffhausen. From Neuhausen it is just a short walk, and you are closer to Beringen.
It is a nice enough area but since that stay in the '70s I haven't stayed there. Either on my in to Switzerland from the Ällgau or day trips from various northern Swiss towns or cities.
Nearby Stein am Rhein is very nice, but again quite small...