I stayed in Appenzell for two days during my nine day road trip around Switzerland in mid-April, 2019. In these two days, I visited Seealpsee, Sämtisersee, and Hoher Kasten. Seealpsee was first on my list, a beautiful lake in the mountains. I ended up spending all day here (about 11am-6pm).
I traveled by car and parked in the large gravel lot just north of Hotel Alpenrose, on the east side of Wasserauen street. It will take you about 45 minutes to hike to Seealpsee from this lot. Simply follow Wasserauen street and walk south along the wide and well-marked trail. Although there are other wooded hiking trails up the mountain and to the lake, this is the safest and fastest way to get to the lake. I saw many families with children take this trail, and although it is paved and only takes 45 minutes, it does get very steep at times.
Once you get to the top, the restaurant will be on your left (Berggasthaus Seealpsee), and the lake will be straight in front of you. This restaurant is not open year-round, so plan on double-checking before you plan on eating there! It was only open on the weekends when I was there in mid-April.
Hiking around the lake will take you about 30-40 minutes. This lake has incredible views, and you should take the time to relax and explore the area! It was one of my favorite stops of my entire road trip. Excluding hiking time, I would spend a minimum of two hours here.
I ended up taking a wooded hiking trail through the mountain on my way back down, which took me about an hour. The start of this trail is on the northeast side of the lake. There was a lot of snow when I was there, but I just followed the obvious foot trails down. There are also a few yellow trail markers leading you down.