I'm in the same boat. We have flights and hotels (pre-paid) that will need to be cancelled. I'm not worried about getting the refund on the United flights since they cancelled the flights in and out of Europe, but I had booked a flight from Athens to Santorini and the hotels were not cheap whatsoever. Hopefully they will issue a refund, or at least let me rebook the same accommodations later.
Update: The hotel we planned to stay at in Santorin (Kirini) said no refund and did not offer credit towards a future stay. This place required advance payment to reserve, so they have me by the nuts for about $4k. This was their response to my cancellation and refund request.
"Greetings from Katikies Kirini Santorini!
Thank you for your e-mail!
Kindly note that we really feel sorry for all the situation that has been raised worldwide and we wish to stop soon.
We hope you and your family and safe.
We would like to inform you that for the time being and according to the Greek Government, our properties will be open normally in June.
Your reservation is reserved under the non-refundable terms and no refund is allowed to be made. Nevertheless, we would recommend you evaluate again the situation due to this issue, later on, approximately 15-20 days prior to your scheduled arrival in order to have a clearer view and inform you of all the best available options we may offer you.
In any case, we will keep you updated and as it has always been, at Katikies Kirini Santorini we are entirely focused on the experience of our guests having your health and safety as our highest priority."
AKA 13-0