We have 2 free days in Vienna and would like to use one to make a 1 day trip to Budapest. The free days are Sunday and Monday.
Does it make a difference which day to choose?
If you have time to spend two days, okay. Truthfully, Budapest is more like a 4 day minimum city--like Vienna.
If you're allotting just one day, stay closer to Vienna and go to Bratislava which is 39 miles by bus. It's a neat, high tech and very high income little city.
Budapest is a great city and worthy of more than one day. However, if all you have is one night, I would leave very early in the morning, stay the night and return to Vienna late in the evening the next day.
Go on Sunday because most of the museums are closed on Monday. A day trip if you must, but the evenings can be special so consider spending the night. I'd suggest the Marriot or the Intercontinental on the Danube for a one night stay, then catch an early morning train back. Takes less than 3 hours.
I'd either spend both days in Budapest or day trip to Bratislava. If I recall correctly, it's a 3 hour train ride to Budapest and 1 hour to Bratislava.