For Alta Badia I can highly recommend Rosa Alpina. The property recently joined LHW. In the same location Ciasa Salares, a 4* superior, owned and managed by relatives of Rosa Alpina. Ciasa Salares has a restaurant with 1 Michelin *. Not truly luxury but nice and comfortable boutique hotel with excellent service.

For Val Gardena/Alpe di Siusi I would recommend Alpina Dolomites (also LHW) over Adler Lodge. Better location, better hard product and better service.