Budapest or Vienna

For a first time visitor I would suggest Vienna. I absolutely love Budapest but I had already been to Vienna twice when I finally went to Budapest. Now if I go back it would be to Budapest. But I still think Vienna would be a better choice for a first visit, unless you're particulary interested in Hungary's history.

We visited both Budapest and Vienna for the first time. I think it depends on your interests. Especially loved the museums in Vienna. Budapest for us was a pilgrimage of history. We hired a guide and it was a meaningful journey for us. We would return to Budapest. We stayed 5 nights in Budapest and wished we had stayed longer!

Vienna is a great European city in the continental style. The palaces and museums there are just fantastic. Until WWI, the Austro-Hungarian empire of the Hapsburgs was immense--all governed out of Vienna. I've been there a number of times in the last 50 years.

One good day excursion from Vienna would be Bratislava, Slovakia. It's only 39 miles from Vienna by train or bus--but a world apart. Budapest is a little far for just a day or so.

We also love Budapest, and have been a couple of times in the recent years. We feel comfortable there, and the food suits our palate well. And we'll return next trip to Europe. It is very inexpensive in comparison with other large European cities.

I asked this question 4 years ago. The responses I received tended to suggest Budapest.

https://community.ricksteves.com/travel-forum/general-europe/vienna-vs-budapest-as-central-europe-destination

We ended up going to Vienna, primarily because I didn't want to help Viktor Orban's economy. Maybe not the best reason to have decided our itinerary, but there it is. Absent that, perhaps I would have chosen Budapest.

Whatever you decide, when your travel date approaches, go on-line and see what is happening. While in Vienna, we managed to see the "Stairway to Klimt" on our first full day in Vienna, the last day that exhibit was "up" (and I do mean up!) https://www.khm.at/en/visit/exhibitions/2018/stairway-to-klimt/

And, about two or three months before our trip, we found free tickets to an Open House that the Vienna Opera hosted that same evening.

For me, Vienna is almost in my first tier of cities (London, Paris, Florence, Rome, Amsterdam). I haven't been to Budapest but I was surprised at how much I loved Vienna. There's lots to see there. The Sunday svc at the Augustiner church near the palace(mentioned in RS guidebook) was as enjoyable as an English evensong.

I'm puzzled by your question about a daytrip. Unfortunately, it conjures up a two-hour ride, each way, from some other great city of the world. You could get away with that for Budapest, IF you planned carefully, at least eight hours solid desk work. But it's an absurd idea for Vienna, if not as absurd as for Paris or London. Here's our trip to Vienna (not, first trip to Europe:)

NYC USA - Innsbruck, Austria 3 nights -train-Salzburg Austria 3 nights-train-Munich Germany -3 nights-train-Vienna, Austria 4 nights-NYC USA

I have to make the observation that this itinerary applies to two penniless college kids with backpacks, just as well as it applied to two young professionals with plenty of money for real hotels. It has little to do with your question, but I personally wish I had visited Prague sooner, and rate it slightly above Budapest. Hungary has moved way to the political right lately, but when we were there, it was still common for cab drivers to speak warmly about US assistance towards democracy.

(Some people go to Mauthausen KL from Vienna, but I recommend Dachau from Munich or Buchenwald from Weimar (that last is probably the quickest and cheapest travel of the three. One is enough)

General Europe advice, blue menu top left:
https://www.ricksteves.com/travel-tips

Budapest. Hungary has moved way to the political right lately, but

I don't give a hoot about politics; all I am doing is trying to have a good time.

Just need to add that the Hungarians (and everyone else) were delightful to talk to during my 2 weeks there last month. No worries about politics unless you start that.

Having a good time? Budapest. I found it fascinating. Vienna doesn’t do much for me but I wouldn’t tell someone not to go. They are just different.

was simply suggesting that the locals are no longer likely to be especially pleased to be talking to an American

We get a similar displeasure from our fellow countryman traveling in some parts America. LOL. We we have been treated worse in America than all our travels in the world and people generally don't know where we are from.

I've been to both, spent much more time in Budapest than in Vienna. I found Hungarians to be more outgoing than Austrians.

Both have lots to see and do. Budapest is cheaper. Using a day out of a (presumably) short stay in one to visit the other is short-changing both.

I'm not sure if you're saying it's your very first trip to Europe or to just those cities.(?) Anyway, as someone who traveled a fair amount before making it to those, I thought Budapest was the more fascinating. I probably wouldn't go back to Vienna again, but I'd like to go to Budapest.

It somewhat depends on what you want to do. Vienna, as the Hapsburg capital, has more and better art and architecture. Budapest, in my opinion, has better food and better nightlife. I thoroughly enjoyed both, so if you have time, splitting it is a good idea. It is a long haul for a day trip, but it would work well to stay in Vienna and do an overnight trip to Budapest (or vice versa).

Budapest is noticeably cheaper if that is a criteria.