The Montelago Celtic Festival is a destination in and of itself, in magnificent Apennine surroundings where breathing Italy's cleanest air is simply part of the deal. But if you're interested in seeing more, there are plenty of options.
In the vicinity
Within the municipality of Serravalle di Chienti, the Varano Vault (Botte dei Varano) is an underground duct constructed by the powerful lord of Camerino, Giulio Cesare Varano, between 1458 and 1464 to drain the Colfiorito plain. During reconstruction of the vault following the earthquake of 1997, another duct built in travertine was discovered parallel to the Varano Vault, dating back to Roman times. Visits to the archaeological sites can be made by arrangement with the town of Serravalle di Chienti.
According to legend, the apostles Peter and Paul sought refuge on a cold and rainy night in the ancient Roman town of Plestia on the alpine Colfiorito plains. The only person to offer help was a young woman, from whom the apostles - out of respect - accepted only bread but not lodging. They then moved off to spend the night on nearby Mount Trella. When they were far enough away, God's wrath descended on the town, and a tremendous earthquake and heavy rain caused widespread death and destruction. When the apostles came down the next morning, they found but a few survivors, amongst whom was the young woman. In remembrance the Church of Santa Maria of Plestia - built in early Romanesque style - was erected on the ruins of the town. The church is located off the SS77 not far from the festival site near the town of Colfiorito.
The Paleontological Museum in the town of Serravalle di Chienti contains the oldest fossil record in Italy of the migratory and evolutionary events that occurred at the end of the Pleistocene era. Amongst the fossil displays from the archaeological excavations in the villages of Colle Curti and Cesi, are remains from the ancient hippopotamus (much like its modern descendant), the rhinoceros, and the African elephant. The museum and archaeological laboratory can be visited Saturday and Sunday from 10:30-12:30 and 16:00-18:00, and on other days by appointment through the municipality of Serravalle di Chienti.
A bit further away (but still readily accessible)
For lovers of nature, mountains, and classic Italian villages, there are so many options that if I really got started I wouldn't be able to stop. So keeping it to just one trip suggestion, take off for Visso just over half an hour away (around 30km/19 miles) in the heart of the Sibillini mountains, part of the central Apennines.
After visiting the impressive 14th-century Church of Santa Maria and sampling the town's traditional salami and cheeses, head on another 25km (15 miles) to the magnificent Piano Grande and the village of Castelluccio, where the area's renowned lentils are grown. One of the best-known hikes among many in the area is Lago Pilato, two glistening mountain tarns reputed to be the burial place of Pontius Pilate. Not far off is Monte Sibilla, home to the cave of Le Marche's very own Sybil, wose legend reputedly spawned Wagner's opera, Tannhäuser. then of course there's Valnerina ...
Just 45km (28 miles) and 3/4 of an hour away is probably the big dog of nearby tourist attractions - Assisi. I could go into why you should go there, but since there's a gazillion sites with information about it, I'm going to acquiesce in favour of those sites. Suffice it to say, even if you're not religious, it's well worth the trip.
A bit more off the beaten track but still in Umbria, Bevagna is a gem of a town undergoing a renaissance of sorts. Just half-an-hour from Assisi and about the same distance from the festival, Bevagna is a classic central Italian medieval town of some 5,000 inhabitants, with replica artisan workshops demonstrating the centuries-old techniques employed to make bells, paper, and other products. In addition, more and more Roman ruins are being discovered, dating back to several centuries before Christ, and if you like a little tipple, Bevagna can offer tastings of the delectable Sagrantino wine - favourably comparable to Italy's superior reds such as Barolo and Montalcino - whose epicentre is at Montefalco just 15 minutes away.
OK, so now we've scratched the surface, do some digging yourselves...