Augustiner Keller on Landsberger Strasse is my recommendation. And just about any of Munich's Biergärten.
A day trip on the S-Bahn to Aying is a good thing. If not, Augustiner Keller, Andechs an Dom, Aying on the Platzl. Many more.
Der Pschorr in the Viktualienmarkt and the Chinese Tower in the English Garden were both a good time for me. I have yet to go to Forschungsbrauerei, but it sounds like a worthwhile visit (also on the S7 line, I think). I also haven't been to the Weisses Brauhaus or Ayinger's place (across from the Hofbräuhaus), but their beers do speak for themselves.
Steve linked a good one. This is from some guy named Ron P. http://www.europeanbeerguide.net/munipubs.htm
Ayinger am Platz (near the HBHaus) or Liebhardts in Aying itself. Andechs am Dom (near the Frauenkirche) or the Andechs Monastery itself. Weihenstephan in Freising. Weisses Brauhaus downtown. Forschungsbrau in the suburb of Perlach.... I prefer the Augustiner Braustubn myself, for Auggie biers.... Prosit!!
While touristy - everyone should hit up the Hofbrauhaus on their first Munich trip. If nothing else, it's like training wheels for the other halls, and the beer is still full-on wonderful. Eat somewhere else (like the Weissesbrauhaus a block away) but hoist some liters at the HBH.
I highly recommend Andescher am Dom. http://www.andechser-am-dom.de/ Great place to grab arguably the world's best doppelbock on tap: http://beeradvocate.com/beer/profile/911/2899
This is what I tell people as well. You just have to go here. Enjoy a mass or two of HB dunkel, and dance to the music if the band is playing. My wife danced with an older local gentleman the only time she went (before we were married) and I sat by a German (not from Munich) couple the last time I was there, so it's not just non-German tourists who visit the place. A bonus is that Ayinger's Speis und Trank is just across the street, so you can enjoy many of Ayinger's offerings if you don't have time to get to the village. And if you're lucky, you can enjoy their helles served Bayerischer Anstich.
At 5:00 everyday Ayinger's Spies und Trunk taps a keller bier, plus the horseradish soup is to die for. For the nightcap either hit Andecher am Dom for a doppelbock or the Weisses Brauhaus for a eisbock.
I took a trip to both Munich and Salzburg about a year ago (actually literally a year ago today). I'd recommend going to the Chinesicher Turm for a stereotypical beer garden experience, though the Englischer Garten is a really nice break from the hustle-and-bustle of downtown Munich. I'd also go to the Schneider Weisse brewhouse, since they have some incredible beers. After downing a liter of Aventinus, I was having a pretty great time for the next few hours. In Salzberg, depending where you're staying, I'd take a visit to a restaurant called "Alter Fuchs"- they have good beer on tap, and if you're up for dessert their Kaiserschmarrn is incredible.
