Tips:
If you stay 3 nights, most hotels and accommodations give you a pass that gets you many free activities. (free rides up 3 lifts including the Ebenalp lift, a free day of e-bikes, free entrance to several museums and the cheese factory nearby, free rides on the trains, free ride on the rodelbahn nearby, etc. etc, )
Appenzell is small and how much you enjoy it can be a little weather dependent. If it is beautiful and you can do all those things for free, filling two days will be easy. Some other rainy day activities: Visit the Appenzeller Brewery that makes the Alpenbitter. It is mostly a store, but you may get lucky and get on an English speaking tour (we did, but they are not often). Ask at the TI about any traditional music shows in the area. (Rick Steves lists one that takes place on certain nights at a hotel. We went to it in 2018 and it was very good.) Also, even on cloudy days, you can ride up the lifts and enjoy the restaurants at the top. (At least if you have the free pass...may not be worth the money without it.) Ebenalp is the most well known and has the famous Aescher hut (as seen on the Rick Steves videos) It is a short hike down to it and can be slippery on wet days.
For a first visit, I would suggest 2-3 nights at the most.
If you are coming from or going to Lucerne or Lauterbrunnen, I recommend Route 8 via the towns of Schwellbrunn, Wattwill, Uznach etc. The area between Appenzell and Highway 3 goes through many charming villages and is much more scenic than taking the highway past Zurich. (which I have also done)
Drive the speed limit. You will not see many cameras, but they are there. Switzerland's philosophy is they don't want you to know where they are (unlike Italy that warns you) According to an article I read, it is illegal to tell people where they are..like in a blog.
Lastly, enjoy your trip!