Fodor's Travel Talk Forums - Recommendations for a 2-day cycle trip

Four of us will be in Switzerland in July for 2 weeks and want to do a 2-day cycle trip.

Considerations:

We will be renting bikes and are happy to do mountain or road biking.
We are open to any region accessible by public transport. That said, we will be in Stein am Rhein before cycling and Zermatt after, so if there is a route that is in proximity to one of those destinations, that would be ideal.
We want to cycle for roughly ~3hrs each day.
We need to do a loop as we will have luggage.
We would like a route that has minimal traffic.
In terms of difficulty, we are seeking a moderate challenge. We are happy to take on a pass if the views are worth it, but nothing too challenging or steep. To give you a reference, I have cycled the Pragel and Klausen passes. We don’t want anything as challenging as these.
To give you an idea of what we are after, we were considering the San Bernardino Pass and the Kunkelspass. We just couldn’t find a loop for the San Bernadino Pass (not to mention it’s out of the way) and the Kunkelpass route we found was a one day loop.
We’d love a route that has grazing cows, traditional towns or taverns along the way and classic Swiss scenery, be it the alps or rolling green hills.
Although we enjoy cycling, it’s more about the scenery.
We’d like a route that is remote and quiet. We will be seeing the big mountain scenery after cycling, so we’d rather cycle a less iconic location/a less scenic or mountainous spot with fewer tourists about.
I’m partial to Appenzell as I’ve heard this area has retained traditional culture, has lots of grazing cows and this is an area we will otherwise not be visiting.

I hope that’s enough information.