Mahr's Bräu is definitely my favourite of the Bamberg breweries, followed by Fässla. A great place to go when the weather's nice is the Stephansberg, a hill just to the SE of the old town. Up there are beer gardens (Bierkeller) from at least three of the Bamberg breweries, including Mahr's.
Incidentally, if the Schlenkerla is a bit too smoky, try the
Spezial; it's also smoked but not as strongly.