maybe you can find some rocky structure near the "grotte di Castro", I have some friends in that area but nobody can give me info about it
maybe also the rocky walls sustaining Orvieto can be climbed ..
edit, if you want to make some fine hikes go to Monte Rufeno (few km N of Acquapendente) you can find info (and good food) at the "Monaldesca", a small country house near Trevinano
... once there tell Angelo you are a friend of mine
From that area, head south to Viterbo, then west toward to coast where you'll fin Ripa Maiala, with around 100 mostly routes on a 30m high crag. They have frequent closures due to wildlife restrictions so you may want to check before making the drive. Its very scenic.
Your other option is to follow the same direction as to Ripas Maiala but on the road south along the coast until just before the town of Cerveteri. There you'll find Furbara with circa 50 routes on a 40m cliff - mostly middle grades. You can also turn north from Ripa Maiala to the area around Obetello but the cliffs are so small you are almost better off sunning back at the lago.
There are also supposed to lots of crags south of Terni but I have no idea where or of what quality.
Technically the Lago di Bolsena is in Lazio but right on the corner where Umbria, Toscana, and Lazio meet.