I recommend Spoleto, a hill town with wonderful views, the site of an annual music festival, an interesting local cuisine, all nicely preserved with lots of winding roads and small footpaths to take you through the city. Also an impressive aqueduct outside town.
Some of the towns recommended here, Lucca, Montepulciano, are in Tuscany, which is adjacent but usually considered more touristy, more crowded than Umbria, but also wonderful.
I've lived in Rome, Genoa, Florence and just love Italy.
I would urge that instead of an agriturismo venue that you find a rental in or very near a town. One of the joys of Italian life is the morning espresso bar, the evening passeggiato, meeting people, and walking to restaurants, stores, train stations. I would not want to be isolated on a farm where you have to drive everywhere.