not a hipster hotel - stay at the gelliert, ask for room 424, or at least 324 - sort of mini suites with porches and good views. seriously, this isn't what you are looking for, but it is an old, serious eastern european hotel with a spa inside, with a fantastic view.
aside from that, you have to spend some time in a spa, and the gelliert spa is probrably the best example of a budapest spa that you will find.
aside from that, I've stayed at the intercontinental and the marriot, both are good. but I strongly advise the gelliert.