The closest airport is Perugia which is about 50 minutes away - Ryanair flies Stansted to Perugia four times a week and the cost is usually excellent value. Perugia is a small airport - from the departure lounge you can see Assisi on the hillside in the distance!
Other options for airports - all of which I've used over the years:
Rome Ciampino is just over 2 hours drive away and Rome Fiumincino is 2 hours 20 away - both via the A1 motorway.
Pisa airport is 2 hours 30 minutes drive away - I've combined the trip with a night or two in Lucca, which is close to Pisa and is one of my favourite cities.
Bologna... I always love flying into Bologna because when I do, I use it as an excuse to stay in the city for a night or two. It's about 2 hours 30 minutes drive to the cottage from the airport. Bologna is a fantastic city which I love! It's easy to get the shuttle bus into the centre from the airport if you like the idea of staying in the city.
Florence airport is about a 1 and a half hour drive from the cottage - again, it's a great way to combine a couple of nights in Florence with a week in Umbria.
You exit the A1 motorway at Querce al Pino or Bettolle - I'll send instructions on exactly how to reach the cottage from there.
An alternative to flying:
Every summer for 8 years I drove to the cottage from the UK... I did this on my own five times, in fact! It's a wonderful drive if that appeals to you - 14 hours from Calais, very straightforward and only busy from Milan onwards... If you're interested in doing this, please contact me and I can explain a bit more about it and suggest places you can visit en route... In the past I've stayed in Verdun, Nancy, Modena, Bologna, Piacenza, Padua..... All beautiful cities!
If you'd rather arrive by train and hire a car locally, there's a station in Castiglione del Lago which connects to Rome and Florence.