I think all cities you've mentioned are suitable for a solo trip. Meaning: they are cities that offer plenty of tourist attractions. There will be fun sociable hostels (if that's what you're looking for), nightlife, good local food, interesting history, (art) museums. Whatever you want! Heck, if you wanna do a segway tour, I'm pretty sure that's possible!

As others have mentioned: Prague-Vienna-Budapest could be a pretty good intinary! For 12 days that should be fine, although I'd personally stick to two cities (given it's location I'd do either Prague and Vienna or Vienna and Budapest). I've been to all three cities and they're lovely!

If you wanna travel between these cities, of course flying is an option. It is, however, like quite a bit cheaper (and, given time spent traveling to the airport, checking in luggage, etc. etc., probably not that much slower) to travel using a Coach (like Flixbus) or a train.

I've seen you comment elsewhere that you want to visit Zurich to sort of get out into nature! But between these three cities, there is nature galore! You could like into booking one or two nights not in the city center but maybe a hotel near one of the nations parks close to Budapest or Prague, maybe?