Prague I can help with:
1st choice for the beer lover has to be "Zlý Časy" which has 36 beers on tap with nearly all of them from small to mid sized Czech breweries. You wont find any Pilsner Urquell or other big "Czech" brands there. Never go after 5PM without a reservation as this place is always crowded, even on week-nights. Also next door to the pub is a shop selling a huge range of bottled beers from all over the world.
Address - Čestmírova 5, Praha 4
http://www.zlycasy.eu/
Then just down the road from there is "Zubatý Pes" which has 15 beers on tap with half being from Czech breweries and the other half from other northern European breweries. This place has a great selection and unlike "Zlý Časy" there is almost always several free tables. I used to live on the same street as this place so have been there many, many times and never had a badly treated beer. For the brave they also have a beer shots from Brewdog which range from 20% alcohol upto 40%.
Address - PETROHRADSKÁ 216/3, VRŠOVICE, PRAHA10
http://www.zubatypes.cz
Next up is Kulový blesk which has 18 taps with Czech breweries beers.
Address - Sokolská 13, Praha 2
http://www.restauracekulovyblesk.cz
All of these places can be reached by tram from the centre in under 15 mins, none are in the slightest bit touristy, have great prices and are very much like a classic pub.
As recommended above Kocour and Matuska are both great smallish breweries and regularly have beers on tap at all these places. My personal favourite being the Raptor IPA from Matuska or Mondeo from another small Czech brewery called Chýně. In fact if you had a car you could go visit the brewery in Chýně and get the beer from its source as its only maybe 45 mins from the centre of Prague.
If you just want a beer and don't fancy trekking to a special place then go for anywhere that offers "Nefiltrované Pivo", "Kvasnicové Pivo" or "Nepasterizované Pivo" which will be much more tasty than the coloured fizzy water that most pubs will serve. In addition out of all of the more widely available beers I recommend you go for anything from "Svijany" which is better than the other big brands most of which are not even Czech any more.