Luxury hotels in Vienna – any recommendations?

Hello everyone,
a couple we're good friends with are planning a trip to Vienna next spring and have asked us for some hotel recommendations. They're hoping to treat themselves to a few nights in a really lovely hotel, preferably somewhere with a bit of character, excellent service and perhaps a nice spa.

I've been to Vienna many times myself, but I've never stayed in any of the more luxurious hotels there, so I'm not much help in that department! I've had a look at a few options online, but I always find personal recommendations far more useful than hotel ratings.

Has anyone here stayed in a luxury hotel in Vienna that they'd particularly recommend? I'd be very grateful for any suggestions, or even places you think they should avoid!