Although the Basilica di Sant'Ubaldo, perched high on Monte Ingino, is a perfectly lovely church, the real adventure is getting there on the funivia. The word funivia suggests an enclosed cable car, but this is more like a glorified ski lift that whisks you up the steep hillside in a hanging metal basket.
To board you have to stand on a red dot and be bundled into the basket by an operator as it swings past. Once the giddiness has worn off, you can relax and enjoy the six-minute ride, watching as Gubbio, which moments before had seemed so impossibly hilly, gradually transforms into a flat little toy town. Beyond, the entire valley spreads picturesquely before you.
There's a cafe on top of the hill by the funivia station, but the nicest way to spend the day is to bring a picnic and have a wander.