"So with that said, does the recommendation change at all?"
Absolutely. With only 8 days on the ground it makes sense to stick to one area, if not one city. Based on what your interests are, I would probably suggest Austria. Split your time between Vienna and Salzburg, with some time spent in the countryside around Salzburg. Most kids would like a boat ride on a lake, an alpine slide experience, the puppet theater at Mirabell gardens, the salt mines, etc. And kids usually love castles/palaces, there's lots of those in and around both cities. Also, both cities have zoos if your kids are into that.
All of your choices are good ones. I loved Budapest and am longing to go back again. I also loved Krakow, Prague, and CK, but others will have to tell you what kids would enjoy there because I don't travel with kids. All the cities you named are strong on tourism and I'm sure they all have lots of fun things for kids and families to do. Just thinking back to when my kids were young and based on what they enjoyed when traveling in the US (no European jaunts for us, unfortunately), I'm pretty sure they would have liked Austria the best.