Side trip from Vienna

What time of year?

Assuming your trip is two weeks from now, it will be cold, so you'll want a larger city with plenty of indoor activities. I'd fly to Berlin as airfares are always cheap.

Yes, 2 weeks from now.
I have not been to Berlin, I would think there are still cheap flights.

Cheapest return flight between Vienna and Berlin: $85 (as of now)
https://www.kayak.com/flights

The train or bus ride would be about 9 hours, i.e. cannot recommend.

I use this:
https://www.google.com/flights/#search;f=VIE,XWW;t=r-Europe-0x46ed8886cfadda85%253A0x72ef99e6b3fcf079;d=2016-11-28;r=2017-03-11;tt=o;s=0;mc=m

but I was surprised at how few discount flights are out of Vienna. If you use the link above, search for one way flghts as the discount airlines only fly on certain days of the week. So, change the day of the week to find the flight out, then work to find the flight back also as a one way on various dates, then combine the dates and see if you get a better deal with a RT flight (but on the discount airlines you generally will not).

Take the train down to Budapest, spend a night or two then take one of the discount airlines (most destinations are under $125 RT, all under $200 rt) to:
Kutaisi, Georgia
Baku
Kiev (my current favorite)
Tel Aviv
Bucharest
Hurghada (look it up)
Athens
Larnaca
Madrid
Malaga
Rome
Milan
London
Copenhagen
Targu Mures
Paris

https://www.google.com/flights/#search;f=BUD;t=r-Europe-0x46ed8886cfadda85%253A0x72ef99e6b3fcf079;d=2016-11-20;r=2017-03-11;tt=o;s=0;mc=m

Graz? Though 4 days might be a bit too much time there.

If you're up for 5 hours on a bus, Zagreb is very nice and has quite a lot of museums.

But I like the Berlin idea best of all. Fabulous city with never-ending sights, the vast majority of which are indoors.

Thanks James E, that map is awesome with flights from Budapest. Flights are not nearly as cheap from Vienna.
acraven- I have been to Croatia, but not Berlin.

Its one of the attractions of Budapest that gets overlooked. Get a cheap apartment, spend a few days, stash the heavy luggage and take a 2 night side trip to some far corner of Europe or Asia; return home to your apartment in Budapest; sit in a wine bar and discuss the adventure for a few more days .........

Or,

Fly direct from the US to the far away corner on an Open Jaw ticket with Budapest as the Departure city and use the discount to connect the two. But you always have to end in Budapest, at a wine bar, discussing the adventure.... Nothing else is appropriate.

@James E.
Love it, thanks for letting me in on this travel secret. I am going to look through all the Budapest flight options.

We've done
Belgrade (arrive in Dubrovnik, then drove through Montenegro to Titograd, then flew a cheapie to Belgrade, then a few days later a cheapie to Budapest.
Bucharest (and most of Transylvania) There are flights to a couple of other cheapies in Romania
Sofia, then drove to Istanbul
Istanbul
Moscow for Orthodox Christmas
Tel Aviv for Hanukkah
Kyiv (and Odessa) for independence day (one of my current favorites.)
Edinburg for fishing
Paris Bastille day
Cologne/Bonn

Next year
Baku in September (or maybe June for the Formula 1 race)
Kyiv again in May
Riga for Christmas