Not only is Budapest cheap but it is also beautiful. Not beautiful in that every building is stunning like in Paris. You don't begin to pay less attention as time goes on, the fact that not everything is perfect makes certain things stand out. For instance, there was a row of three buildings with 2 gorgeous spires each, only one had been damaged and replaced with a hideous black box. A lot of buildings do have the most amazing tiled roofs though.
Fisherman's Bastian, View from the Castle Grounds, Matthias Church and Castle of Vajdahunyad
My other half live miles away from me so any time together is always good but we had an amazing time wandering the streets in the sun to see the castle grounds (including the Fisherman's Bastian), Heroes' Square and all the other touristy sites. We spent the one rainy day in Gellert Baths, which most would find amazing but that I wasn't massively impressed with, before wandering to see the stunning Parliament buildings. We also spent a fair amount of time drinking lots of not so lovely wine and beer. You should go, see it all and watch out for Unicum. It is a very common spirit, not all that pleasant and is sure to give you a hangover.
View from the Castle Grounds
St Stephen's Basilica