It was impossible for Batman not to be curious about magic. Someone like him was born wanting to investigate everything thoroughly, then devise several sets of solutions for any situation that might arise.
Since meeting Constantine, he had slapped two labels on that scumbag: one, an irredeemable piece of human trash; two, a source of information that could help him understand magic.
To investigate someone, he naturally had to first understand their daily routine and movements, and the best way to figure all that out was to follow them.
Batman had encountered people visiting certain difficult-to-describe places while handling such matters before. Or rather, when investigating certain people in Gotham, those places were impossible to avoid.
Such places inevitably involved certain less-than-legal businesses, though in Gotham, their existence would not surprise anyone.
The only exception among them was that Psychology Professor. The professor's rigid routine between two points had even made Batman prepare a contingency plan in case he was a robot. But aside from that professor, everyone had some little hobby, and Bruce's friends were no exception.
Harvey Dent liked playing pool and would go to game rooms with his courthouse colleagues after work. Gordon went drinking with his coworkers and hunted in the countryside during his free time. Catwoman, though a thief by trade, went to dances or amusement parks when she was not stealing. Since every place they visited was run by the Mafia families, each one had some shady dealings going on inside.
When investigating those people, Batman would usually knock someone out if he saw such transactions. If things went too far, he would speak with the boss of the establishment. But those places only occupied a small part of those people's lives.
Constantine was different. Those businesses made up his entire life.
Bars, dance