I made a trip in Europe this summer. I went to Austria then Czech Republic. I would recommend:
Prague: Go to U Fleku. The waiter will try to rip you off with Becherovka (sp?), but focus on the beer. ***(see the end for explanations) The beer is amazing. The best beer, by far, on my trip. A very refreshing chocolate-coffee bohemian dunkel. Amazing. You can buy bottle version of this beer (750 ml, 1.5 l swing-top and 2.5 l) on place. But they are not nearly as good as on tap, in U Fleku itself. Even my girlfriend still talks about it...
The other very good place in Prague I found was the Strahov monastery. The beers were excellent (the bohemian dunkel was close to U Fleku's one, but not as perfect).
If you go in Austria, in Vienna, as MattHollingworth said, you can try the 1516 Brewing Company. There seems to be some amazing beer, the ambiance is good, but the hefe weiss was meh. The blackberry ale too. Otherwise, you can find some good austrian beers in supermarket. In one, named Billa (they are all over austria, but the beer stocks vary from one Billa to another), I found Franciskaner Weiss and Edelweiss, two very good weissbier.
In Salzburg, Austria, you can try the Augustiner Brau's Bier Garten. The place is cool, the beer is good too. Stiegl Brauerei is meh, but if you happen to buy the salzburg card, you have like three free beers there, a gift (a glass or a bottled beer) and a free visit of the museum. I don't have good memories from Stiegl, but it may be because I lost myself while trying to return in the hotel with the bus system...
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***: Basically, a guy first came and gave me and my girlfriend a beer. Very polite. A good waiter. Then, another waiter came after the first one, and asked us if we wanted a Becherovka. This one was less than polite.
Waiter: "Do you want a Becherovka?"
Me: "No, thanks..."
Waiter: "It's a Czech tradition to drink this before drinking a beer"
Me: "No, really, I don't drink liquor..."
Waiter: "Come on, you got to live the Czech tradition!"
Me " Really, no, I hate liquor..."
Waiter : "Ok, then, just take one for the two of you!"
Me : "No, we don't want to."
Waiter: "Oh come on!!!"
Me: "No..."
Waiter: *BIG SIGH*, took a sheet of paper and made two lines (two beers) and got away. He came back, after the first beer, but he understood really fast the second time...