We just spent 10 days in Greece, on Mykonos and Naxos( loved Naxos.. Mykonos not so much.. too pricey )
We encountered nothing but Greek hospitality.. and saw nothing but beautiful beaches.. flowering bushes against white washed buildings..
We returned about 2 weeks ago.. and it surprises me how many people ask about "the refugees".. honestly.. you are not going to see or encounter any unless you go to Athens and look for the camps.. or perhaps if you visit the islands in the chain nearest to Turkey.. and frankly that is not where most tourists go.. and even if you did.. what on earth are the refugees going to do to you .. nothing has been reported except locals helping them.
I would go back to Greece tomorrow.. and btw.. my daughter, who is only 19 ,, just spent two weeks there with her friends backpacking around ( so not with us) in early May and they felt very safe.. encountered no issues.. and had a ball.. they visited Corfu and Santorini.. so when I say I think you will be perfectly safe I am not just trying to calm you down ..
Go and have fun.. and visit Naxos.. the people are amazing( our rental car broke down in the mountains.. middle of nowhere and locals helped us.. gave us food, drinks, and phoned the rental car company for us.. these people are so nice) ... the food great..( and cheap) and the beaches so beautiful..
Ps I don't think ISIS is that interested in Greek islands.. I think big cities like New York, Paris, London etc would be more their style.