Abbey is a good suggestions. Also, next time, try Abraxas (just S. of 5th on the beach) or farther away, (when it opens again) the Wetlab (Virginia key University of Miami campus, Weds-Fri 5:00pm -> ??). There are others, but I don't know them well enough to recommend.
The wetlab is my local and there is a great selection of micros on tap and bottle with a few locals. Currently, the licence is being switched and I'm not sure when it'll reopen.
On the subject of burgers and beer, I have always suspected they water down their draft... Beers I know pretty well don't taste like they should.