First time visit, then I'd recommend that you stay at the Marriott AND visit the Boscolo - the atrium & the New York Cafe are not to be missed.
Assuming you take the hop on/ hop off bus tour - the Boscolo is en route
Final thing - don't make the mistake of going into "tourist" bars
For example - 0.5L Soproni
Tourist Bar - 1,400 HUF
Local Bar - 420 HUF (and that's expensive!)
Enjoy your time there, it's a beautiful city