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The vines above Spiez bay are worth a walk even if you are not going for a tasting. The slopes put the castle and lake into a different frame, and the wine gives you something made right here to ask about over dinner.
A vineyard stroll and a hosted tasting are separate plans. Check the public tasting dates or arrange a visit with Spiezer Alpine Weinkultur in advance. Confirm the meeting point; do not assume it is the castle. Wear shoes that work on sloping paths, and leave the car behind if you are tasting.