It's not quite what you asked about, but my best meals in Krakow were at two places that I found in the 2012 edition of Rick's Krakow, Warsaw & Gdansk book, but that have been removed from later editions. However, places that I did not like nearly as much (they were OK but not great) have been retained. I have no idea why these two places have been removed. One serves Polish food, the second is fancy but Italian (so, not the fancier Polish food experience you seem to be seeking).
The first was Polskie Smaki, a very nice milk bar serving basic Polish dishes. It's more basic than you seem to want, but it gets a diverse group of locals, and had a very homey atmosphere. While it's not a place that encourages lingering, it was much warmer and more inviting than Rick made other milk bars sound (there was nothing depressing or stark about it). The staff spoke enough English to explain the dishes, and it was so cheap that if you didn't like something, you could afford to get something else in its place. It was so delicious I went twice! Be sure to try the zurek (translated as "sour soup" but actually meaning made from sourdough - wonderful). http://www.polskie-smaki.pl/en/
The other was an Italian restaurant, Aqua e Vino. This was fancy, and while expensive by Krakow standards, it was definitely cheaper than you would pay in Italy (or the US) for food of this quality. https://aquaevino.pl/en/