Vienna would be on my list. And I know you said you wouldn't want to go longhaul, but with other suggestions like Istanbul, what about heading west to Newfoundland?
You mentioned Canada for your honeymoon - Canada's huge. If you are doing the cities, then the parks and reserves near St. John's in Newfoundland might be a perfect alternative. By late May it will be very nice there, and if you two are outdoorsy people, it would be a great spot. Spectacular camping which would keep accommodation costs down. Don't know if you both are into that sort of thing.
5:30 flight time, nonstop from LHR on AC.