Davos is surrounded by mountains and there are many cable cars that can take you up for a good view. However, that can get expensive and I didn't get enough blue sky to make it worthwhile. During the summer, hotels provide a Premium Card if you stay in town for at least a night, which offers significant discounts for ascents around town. This is similar to St. Moritz, although that card offered free cable cars around town but you need to stay for 2 nights.
For a free but nevertheless nice vantage point, head slightly uphill from town to Hohe Promenade. There is a wooden overpass above the Schatzalpbahn track with a wide view. While it was a little slippery to get uphill, the path itself was clear even in the middle of winter.
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