Can you buy and drink a beer (such as Miller or Budweiser) at a bar owned by non-Jews?
According to the Shulchan Aruch (YD 114:1) it is forbidden to drink beer in the same place as non-Jews do, i.e. bars. This is not a kashrus concern, but rather is forbidden out of concern that Jews will come to socialize overly much with non-Jews and come to eat with them. The Rama there writes that the custom in ashkenaz was to be lenient on honey and wheat based alcoholic drinks. However, barley based alcoholic drinks (such as beer) remain forbidden. (The Shach understands the Rama to be permitting barley as well. The Gra and the Peri Chadash there both reject the Rama's leniency.)
With regards to other hard liquor, there is a difference of opinion. Some achronim (Aruch Hashulchan 114:11 among others) say that drinks like rum and cognac are permitted to drink at bars because they are very expensive and were not a part of the original decree not to drink. However, in our times this might be a difficult case to make considering that these drinks are very commonly consumed in bars (see SHU"T shevet halevi 2:43).
Some authorities (chochmas adam, pischei teshuva ibid.) actually assume that this decree includes drinking tea and coffee in coffee shops with non-Jews because the same issue of socialization is a concern. There are some poskim today that actually reccommend not drinking in Starbucks because of this. However, many are lenient on this point.
However, it should be noted that all of the issues above are not applicable if you take the beer out of the bar and drink it elsewhere (see Shulchan Aruch ibid).
As most kosher agencies will tell you, any plain, unflavored, domestic beer poses no kosher problems. The ingredients are straightforward and all kosher, bishul akum isn't an issue (that's another topic), and the prohibition on non-Jewish wine was only on grape products.
As discussed elsewhere, you are allowed to use a clean non-kosher cup for cold food (but not to use the same non-kosher cup on a regular basis). So the bar's glassware is fine, assuming it's clean.
The Gemara had discussed a separate prohibition of socializing with non-Jews over alcoholic beverages; there's much discussion as to what happened to this prohibition (or in what context it applies). Ask your rabbi about this, as well as whether barhopping is a good idea spiritually in general.
The restriction against drinking non-Jewish wine does not extend to other alcoholic beverages.
So assuming the beer is Kosher, it should be OK to drink it in a non-Jewish owned bar.
However, if they also serve wine or non-Kosher beer, you may need to bring along your own cup or drink from the bottle/can.