Take a look at my trip report on Krakow; click on my name to find it. I mention a few restaurants where we ate, and we liked the braised vegetables on the main square.

Krakow = Pod Baranem

Polish cooking greatly exceeded my expectations (sorry for doubting you, Poland!) and Pod Baranem was the best restaurant we ate at in Krakow. Traditional Polish cuisine in a retro, somewhat funky, setting. What these folks can do with wild mushrooms will amaze you.

And I would walk 10 miles - right now - for a good "Zurek" - a soup made from a sour rye base with smoked sausage, potatoes, vegetables and a (or two) hard boiled quail eggs. Yup, Pod Baranem had the best one.

YUM thanks

We enjoyed a floating restaurant called Marina in Prague, on the river:

http://www.grosseto.cz/en/marina-about-us

Nice views, nice food, what I'd call semi-casual dining.

Lavandula

Prague SaZaZu - fusion cooking at its best.

In Krakow, Pod Aniolami located just off the main square toward Wawel Castle.
http://www.podaniolami.pl/en

This was one of the best dining experience we have had on any of our travels in Europe. Partly because it was at 15:00 and we had the Garden room practically to ourselves for the 2.5 hours we were there. Partly because our group of 8 was fantastic company and partly because the food and service was excellent. Capped off with a very reasonable tab of about $25-30 (US) for a full dinner with desert but no wine.

The perogies were great and the Polish shortbread desert was fantastic.

I measure all other European dining experiences against this one but for us all things came together that day.

I'll write as a former Krakow student If you want to taste something that almost every person living in Krakow knows try this:
http://krakow4you.net/restaurants/u-endziora.html

It's not a restaurant, it doesn't have tables, even chairs...but it gathers many people what creates a special atmosphere Especially at 1 or 3 AM, when after a beer or two it is the only place where you can eat something warm and tasty. I always recommend it to my friends visiting Krakow.


Monika
http://geographers-eye.blogspot.com/

And another one, also with a special atmosphere:
http://www.tripadvisor.co.uk/Restaurant_Review-g274772-d942482-Reviews-Kielbaski_pod_hala_targowa-Krakow_Lesser_Poland_Province_Southern_Poland.html


Once gained the award as a best restaurant without a room in Poland

Monika
http://geographers-eye.blogspot.com/

For Budapest have a look at this website. http://www.carolynbanfalvi.com/ She is an American food and wine writer who lives there. We enjoyed her suggestions last spring. We stayed at Cafe Gerlozcy which is a hotel and a lovely little restaurant. http://www.gerloczy.hu/cafe_and_restaurant/

You might take a look at my trip report from 2011 -

www.rimerson.com/Europe-2011/prague/prague.html
www.rimerson.com/Europe-2011/budapest/budapest.html

In Prague the U Horcha for lunch was a hoot.
In Budapest Bor la Bor was quite good and reasonable.

Fantastic, thank you all.

Aussiedream - about 10 years ago we took a trip to Budapest and stayed at a hotel near a square that was then called Moscow Square but is now called Szell Kalman Square. For dinner one night, we and another couple wandered through some side streets off the square and decided to try a little restaurant we just happened upon (whose name, unfortunately, I did write down). Nobody in the establishment spoke English and none of us spoke Hungarian, but we were somehow able to communicate and had one of the best meals of our life for under $10 USA. A memorable dinner, indeed! So - if you are near Szell Kalman Square, I suggest you wander around and try one of the little local restaurants in the area.

for Prague have a look at this Blog .lots of great resturant reccommendations in there.
http://czechoutchannel.blogspot.co.uk/