I disagree meeker, running is harder on the knees than simply carrying around extra weight on a daily basis. The fact is there is sound science behind recommending overweight individuals to not run, not just some blatant "fat people discrimination" on the part of the trainer. Like jerihurd said, running is extremely high impact - 25 pounds of extra weight puts 100 pounds extra load on your joints when you're just walking around, which shoots up to 250 when you run. That's a lot of wear and tear.
Biking, walking, swimming, and elliptical are all lower impact cardio activities.
But as always I say to get the most bang for your buck in the gym lift free and lift heavy (variations on squats, deadlifts, overhead pressing). It's way lower impact than any cardio activity regardless of how much weight is on the bar, and the degree to which it forces your body to adapt to stress burns waaay more fat over time than any cardio activity. Plus you build a lot of muscle, which again, helps you burn that much more fat. And in non-steroid-enhanced women (I'm assuming most if not all of you), it's dense, shapely, hawt muscle, not grotesque, veiny, boxy muscle.
Okay, weightlifting rant over.