I liked all the Ukrainian cities James mentioned, and Kiev probably could keep you busy for 2 weeks if you're adamant about staying in one place. I am clueless about November weather anywhere is Europe, so I don't know how it would compare to what you had in Budapest. Research for my trip this year indicated that Budapest would be warmer than Prague in May.
I'm a big fan of both Romania and Bulgaria but prefer the secondary cities to the capitals. I think 2 weeks would be way too long for me in Bucharest or Sofia, but I confess that I gave each city only about 24 hours, which wasn't a fair chance.
I spent 5 weeks in Poland this summer and loved it. Warsaw was more attractive than I expected (though it cannot match Krakow and Gdansk), and it has many, many 20th-century historical memorials/museums that can keep a person busy for a long time if she is interested in that period (as I am). November weather in Poland, though...
Berlin also has enough for 2 weeks if a person is a 20th-century history junkie.
Prague is an obvious possibility. Everyone talks about the crowds, and they are certainly beyond annoying in some areas. However, the city has a lot of attractions that were not overwhelmed even in August. Over the course of a 2-week visit you'd spend a lot more time in the less touristy areas than in Tourist Central unless you chose to keep revisiting the Old Town.
It would be a different type of experience, but I found Nice a very nice 16-day stop in May 2017. (I was taking 3 hours of French lessons each weekday.) If you enjoy art, the city itself could keep you occupied for at least 5 days. The rest of your time could easily be filled with side-trips even if you are limited to public transportation. Nice is relatively inexpensive outside of high season, and both the local trains and buses along the coast are pretty cheap.
I wonder whether Seville would work? Or Rome?