As going with kids next week I wonder which of the one one is better in respect of:
Scenic, easy (too uphill) , safety (cycling on road with many cars)
Steinegg - Weissbad- Schwende- Wasserauen- the same way back to Steinegg. Seems all flat but is it scenic?
Steinegg- Eggerstanden- Appenzell- Steinegg.
The same as (1) but adding Triebernstrasse/Egg junction as looks photogenic but driving on the road with no edges on side.
but driving on the road with no edges on side
This is what cycling in Switzerland looks like most of the time—riding on a road without shoulders. Since cycling is extremely popular, motorists are very accustomed to watching out for cyclists and will pass you when it is safe to do so.
It is beneficial to familiarize yourself with the rules of the road so that motorists can safely predict your actions. Make sure you understand the various road markings, who has the right of way, and similar regulations.
I regularly cycle, though not in Appenzell, so I am not familiar with the routes you are mentioning. If you are renting bikes, consider getting e-bikes, which allow you to cover a much larger area with the same amount of effort.
Here is where you can find cycling routes in the area:
https://schweizmobil.ch/en/cycling-in-switzerland
You can also take a look here - she discusses cycling, has photos of the route signs, and shares links for rules of the road (the link says with kids, but has relevant info for everyone):
There are several market cycling paths around Appenzell, use one of the many cycling apps to check these out and use Street View from within these apps to see what the scenery will be like.
