This is a recommendation, not a question. As another conclave will soon be underway to choose a successor to Pope Francis, I thought I would recommend a visit to Viterbo, and more specifically, to the Palazzo dei Papi. Viterbo was the seat of the papacy for a period in the 13th century, and hosted a conclave that took 3 years -- from 1268 to 1271 -- at the Palazzo dei Papi. It's now a museum that tells the history of the conclave, and has great artifacts like the actual note sent by the locked-in cardinals pleading to let one of them out. It's a fascinating bit of papal history well-told. I just visited last month and loved it.
Viterbo is in northern Lazio, about 1.5 hours from Rome on hourly local trains. You could walk to the Palazzo and other sites easily from Porta Romana train station. It's an amazingly historically intact medieval town, both within the original city walls and outside of it, with tons of fascinating architecture and fountains. It doesn't feel like a museum, because it's still a living town.