Can you fly direct from Catania (Sicily) to Perugia?
 

Both airports are listed on website but it won't get me a flight. (CTA and PEG)

http://www.nanakflights.com/airlines...ia-flights.asp

Any other airines to try?

If you look at Perugia airport website map of non-stop flights, it shows Ryan Air from Trapani.

http://www.airport.umbria.it/en/flights/destination-map

Just looked at your Nanak website. It's just an online travel agency in Canada.

If you can adjust your Sicily plans, Ryanair flies from Trapani to Perugia a couple of times a week.

Trapani won't work, my niece is studying in Ortigia, so would fly out of Catania

Probably her best option would be to fly to Rome and take the train from there to Perugia.

There's also a bus from Fiumicino airport to Perugia.

I think there are flights from Catania to Florence airport. Train from Florence to Perugia would be a bit more than 2 hours, depending on timing (plus you need to get to the train station from the airport, between 25-35 minutes).

We're actually staying in Bevagna, Perugia seemed to be the nearest airport

Foligno seemed to be the closest place for us to pick her up if she took a train. But I guess she has to take some special train to Termini in Rome and then get another train to Foligno?

I was trying to make this simple and fast, but not sure that's going to work?

The "special train" from FCO to Roma Termini is just the Leonardo Express that operates twice an hour between the airport and Termini and takes 32 minutes. From Termini to Foligno is, with a couple of exceptions during the day, a regional train that takes a little less than 2 hours. The fast train (I only see one departure at 5:40p) takes 80 minutes.

"Simple and fast" just don't compute with the starting and ending points you're working with, unless you want to drive down to FCO to pick her up... You could also meet her somewhere on the train line between Termini and Foligno. Check which trains stop where, but I think they all stop at Terni and Spoleto, some at Orte.