Question Best Places to Stay in Innsbruck and Appenzell?

Hi everyone, my husband and I will be in Innsbruck and Appenzell, Switzerland next August. We're looking for recommendations on where to stay in both places. We prefer accommodations that are cozy, have a local feel, and are conveniently located for exploring. In Innsbruck, we're interested in being close to the Old Town and the mountains. For Appenzell, we'd love to stay somewhere that offers stunning views and easy access to hiking trails. Any suggestions for hotels, B&Bs, or even unique stays like chalets? Also, if you have any tips on what to book in advance, that would be super helpful!