Budapest

It is doable, but it will be a long day.

The train ride is 2:40 hours each way. If you take the first RJ (RailJet) in the morning (7:42am) and the last one back (5:40pm) you will have roughly 7 hours for Budapest. Taking the EN (EuroNight) instead allows you to extend this to 11 hours (6:40am and 8:40pm). (I would not go using a D train which has not so modern cars.)

My highlights in Budapest:

Castle Hill, including the Hospital in the Rocks (https://www.sziklakorhaz.eu/en/, https://en.wikipedia.org/wiki/Hospital_in_the_Rock)
Parliament building (https://latogatokozpont.parlament.hu/en/home, https://en.wikipedia.org/wiki/Hungarian_Parliament_Building)
City center (Váci utca, Vörösmarty tér), including Café Gerbaud (https://gerbeaud.hu/en/, https://en.wikipedia.org/wiki/Caf%C3%A9_Gerbeaud)
Great Synagogue (https://en.wikipedia.org/wiki/Doh%C3%A1ny_Street_Synagogue)

This is only a small selection of sights. E.g. for going to one of the famous spas you would need more time (http://www.spasbudapest.com/).

Get acquainted with public transport. It is easy to use the metro and/or the tram. Just walking would consume too much time.

It's too far. Using the above info, you still have to get to/from the train station in Vienna, so it's another 1/2 hour in Vienna coming and going, and you have to allow time in Budapest to get to/from the train, cutting into the 7 hours you have. You won't want to be late for the train back, so for the last hour, you'll be (or at least I'd be) distracted worrying about being at the station in time. The earlier option means a really long day.

During your time in the city, you'll have to get local currency and figure out how to use local transportation. Budapest deserves more than a few hours. Save it for when you have at least 3 nights there.

People do 2.5 hour day trips all the time. This would be no different. There is nothing wrong with any of the train carriages between Budapest and Vienna, so take the last train out at 8:40pm.

Of course, better to spend the night and take an early morning train back. Budapest is great at night.

If you decide yes, let me know and I will help.

In 2014 I considered doing Budapest as a day trip from Vienna--wanted to see where my grandmother came from. Then I realized how easy it was to just take the train and stay a few days...Budapest captured my heart and I have since returned 4 times. So, be careful...a day trip will most likely leave you wanting more!

I stumbled in, in 2002. But I guess you know that story....