IMO exercising first without changing your way of eating first is a waste of time and may even cause you to gain weight if you eat excessive carbs. If you are obese you are more likely more prone to injury, and may become miserable trying to exercise. Lose a decent amount of weight first--as you become lighter and it becomes easier to move, gradually increase your activity. This is just common sense.

As far as "working off" those problem areas, I believe that is a myth. Most people fail because rather than lose the fat in those areas, they build up the muscles. You can't specify which fat in your body you want to burn. If you stick to a low carb diet you will eventually burn all the excess fat in your body.