Park Hyatt Vienna is pretty unique, but there are a few properties that get you close in vibe and quality.
Hotel Sacher if you want old school luxury and prime location. It’s classic, polished, very Vienna, though a bit more traditional than Park Hyatt.
The Ritz-Carlton Vienna is probably the closest modern luxury equivalent. Big rooms, solid service, good location near Stadtpark. It feels a bit more businessy, but quality wise it’s comparable.
Hotel Imperial is another top tier option if you’re into grand, historic luxury. Very formal, very elegant, and absolutely a five star experience, just not minimalist like PH.
If you want something slightly more contemporary, Palais Hansen Kempinski is also worth a look. Still luxury, but calmer and less tourist heavy feeling.
If you end up using Chase UR through the portal, Park Hyatt might still price okay, but I’d personally check Ritz or Kempinski first if PH availability is rough.