Umbria begins about ninety minutes north of Rome, and the first thing you meet is Orvieto, standing on a plug of tufo above the plain. The cathedral front is one of the great pieces of Italian Gothic and the Signorelli chapel inside it is a fresco cycle of the end of the world, one of the great pieces of Italian painting on the way out of the Gothic. Underneath the town there are caves, wells and Etruscan tunnels going down through the rock.
Just over the Lazio border below it is Civita di Bagnoregio, a village on a pinnacle of eroding clay reached by a footbridge, slowly losing the ground it stands on. It is small, it is astonishing and it is best early or late.
East of there, the Nera valley: the Marmore falls, which the Romans cut to drain a marsh and which still fall in three stages, and around them rafting, canyoning and climbing. Narni, on the way, has an underground complex including an Inquisition cell that local cavers found by accident.
All of it is inside two hours of Rome, and all of it holds a full day.
The three grids are three different days and the mistake is to try to hold two of them together. Orvieto and Civita are the cathedral-and-hilltop day. The Nera valley is the water day — the falls, and rafting and canyoning under them. The underground is a thread that runs through both and is the one that works when the weather does not.
Orvieto is the one to pick if you only take one. The town sits on a plug of rock with a funicular up to it, everything is walkable once you are there, and it stacks a cathedral front, a fresco cycle, a well cut in a double spiral and a second city of caves and Etruscan wells underneath into an area you could cross in twenty minutes. The country around it — Castiglione in Teverina, Amelia, Lugnano — is wine and olive country and is where the tastings are.
Two things to check before you set out, and both are on the cards. The Marmore falls run to a release schedule set by the power station, so arriving between releases means arriving at a cliff. And Civita is reached on foot across a long footbridge, which decides whether it works for everybody in your party.