Hi! is your daughter at UGA Cortona? I taught there last year! Cortona is really nice at easter. You should book your hotel or apartment rental sufficiently in advance (ie now would be good) because it is a busy time for italians to travel, too.
For easter in cortona they do an important procession of religious statues and a ceremony in the main piazza; this is a cultural event not to be missed. One of the spring term professors at UGA has made some films of this event as well as other cortona-tuscany films that you can see on vimeo: http://vimeo.com/833874
In cortona itself there is not too much to see in terms of greatest hits but it has an important etruscan museum (i wrote a bit about that here: http://ow.ly/15PnL) and also the diocese museum with a good painting by Fra angelico. There are a million churches. And if the weather is good there are lots of walking trails. ANd of course you'll have an experienced guide.
Few things will be closed, as the few stores and restaurants in cortona cater to visitors, and easter is an important time for them. You should not worry. Only easter monday shops will likely be closed but the rest of the time you're fine.
I'm so glad I could help! Enjoy and happy easter ;-)
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