You wouldn't be able to do it on a hostel budget, but you did say money wasn't a big issue. I've heard rave reviews about the Hotel Pulitzer. It's a stretch of converted row houses alongside a canal in the old city, but it's an SPG property, so you're getting all the modern ammenities.
http://www.starwoodhotels.com/prefer...propertyID=100
As for Istanbul, I recommend the Hagia Sofia, taking the ferry to the Asia side (watch for Dolphins in the Bosporus), Dolambache Palace, the Basilica Cistern, and the Grand Bazaar.
In Vienna, I'd recommend going to a show at the Staatopera, eating Imperial Torte in the Hotel Imperial, and the Schonbrunn palace.
Any more specific Istanbul/Vienna questions just ask.