I will keep this brief since my sentiments echo most of what Globetrotter already wrote.
Bamkraxler seems to hold a special place in the hearts of the old-school beer hunters in Vienna. There are many newer bars with much larger selections, but Bamkraxler still manages to remain noteworthy.
The main pull here is the barrel aged Augustiner. It is a bit of a novelty in my opinion, but novelties are a big part of beer culture. Bamkraxler also has the nice, airy atmosphere of a biergarten as was explained in the other review.
The food is ok, but maybe a bit overpriced. I've enjoyed the goulash when I had it. The meat was exceptionally tender.
I would not suggest this stop to tourists coming to the city for a short stay, but it is worth it if you live here. I would suggest combining it with a climb up the Stadtwanderweg 1 path to the top of Kahlenberg. Maybe stop at Bamkraxler before or after the round trip.
Bamkraxler is unique: a family-friendly restaurant with a major focus on good beers. It is located in the far north of the city, at the end of the D-tram and at the base of the vineyards. Vienna is famous for it's "Heurige" wine places; this is Vienna's only Beer Heurige.
Nice old two story building on a cobblestone street. Enter through an archway into the large garden with many a table, a playground and a large outdoor grill during the warmer months. The inside is divided into two rooms, the first with a small bar and seven or eight wooden tables, the second large enough to seat about 150. Lots of wood everywhere. No noticeable music. The service is decent, by Austrian standards. They do a pretty good Sunday brunch, have live music regularly in the evenings, and children's entertainment in the afternoons. Closed Mondays. The food is better when the grill is working, but still not bad, albeit rather standard drab Austrian fare.
The flagship beer is the delicious Augustinerbräu from Salzburg, served both in regular kegs and every evening starting at 5:00 from a wooden cask. Other tap beers are from Ottakringer, but there is also a small but interesting selection of German and Austrian brews, including Schneider Weisse, Innstadt Hell, Hirter and Murauer. The beers are always kept and served well in the appropriate glassware. BAs in Vienna with or without kids will definitely want to seek out this place as a chance to indulge our hobby while the rest of the family has fun, too.