It is possible to go through historical centre in even just one day, because everything is so close togehther, but Prague is that beautiful that I think 3 days for someone who has never been there might be even not enough. Hope you'll enjoy our beautiful capital :-) Prague merits 3 days minimum, plus another day for Cesky Krumlov. Krakow, Budapest, and Vienna need three days each, at least. This will give you enough time to savor the places and visit the countrysides as well. You might be able to squeeze in Slovenia.
Because this Prague itinerary is for one day only, I’m going to leave out any suggestions of going inside museums, castle or other attractions. Unless it’s raining or you have a specific interest in a particular museum, there is really not enough time to see everything. And besides, the view of Prague, whilst walking around is truly

Morning. Start day two of your Prague itinerary with a visit to Prague Castle. This vast complex features architecture from Roman-style to Gothic to 20th century. While it may not be the most beautiful castle you’ve seen, it is the largest castle complex in the world, covering almost 70,000 square meters.

I think leaving on New Year's Eve without taking part in the celebration would be a missed opportunity. Depending on how much you decide to see each day, two or three days in Prague would be enough to see the main attractions. I haven't been to Vienna yet. Budapest has the most to see of the three cities. But yes, 11 days is probably enough.
The Historical Charm of Prague. Prague, the capital city of the Czech Republic, is known for its rich history and stunning architecture. With its fairytale-like castles and Gothic cathedrals, Prague offers a unique blend of medieval charm and modern vibrancy. Day 1: Exploring the Old Town
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is 3 days in prague enough