Did I miss something during the movie?
How did Batman know where Martha was? Even Lex didn't know that.
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You may remember an earlier scene in a bar after a bare-knuckle fight, where Bruce, during his investigation of “the White Portuguese”, clones the mobile phone of the head goon who later kidnaps Martha.
This allowed him to track the location of this criminal. It may have also revealed that the criminal had kidnapped Martha, or Batman might have deduced/guessed that he’d be responsible.
If my memory is correct, Batman didn't know where Martha was, rather Alfred provided the location (using Batman's extensive resources). @Shokhet notes in the comments:
"Alfred specifically mentions the phone location, and the fact that Batman is locked in on it"
It's worth noting that Batman is the ultimate detective, knows the area well and as pointed out by Paul D. Waite had been investigating the persons involved (including cloning the henchman's phone, and stealing files from Lex).