Recommend the Hilton Budapest in Castle Hill, definitely 5* property, very romantic. They treat Gold/Diamond members very well. Gold/diamonds are upgraded to Executive Floor with fantastic views over the Danube River. Diamonds may be upgraded to suites (not Golds). The Executive lounge is fantastic. Really good breakfast, open bar with snacks in the evenings. Service throughout is great.
Budapest is great, lots to do and see. People are very friendly and though many don't speak English (and Hungarian is really tough), they try their hardest to help. Has joined the EU but is not on the euro yet so still fairly cheap. Should see it before the tourist hordes overrun it (the airport is being expanded to allow for more budget airline flights) like they have in Prague.