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Begin on Obere Hauptgasse and look above street level. The raised pavements give the shops a second storey of entrances to explore. Wander towards Rathausplatz, then make your way down to Mühleplatz for something to eat beside the Aare.
The castle can be your next stop, but a town walk and lunch are already a good outing. If cloud hides the mountains, there is still plenty at street level. Check museum opening before counting on an indoor visit; walking through the old town and visiting the castle rooms are separate plans. The official town guide gives more detail.