Well you say that your dinner could be "anything" so it's hard to tell really, you could be stuffing up on all kinds of things! Also, try to stay away from white bread - or bread altogether really. Any exercise is good, so running/walking is fine but you don't even really need to go to the gym to do that. If you want to increase muscle tone as well then using the weights in the gym would be a good idea, and perhaps some resistance machines at first to get started. Yoga and pilates would be good for general core and posture, though depending on the level I'm not sure you'd burn much fat in doing so...
I don't want to put you off but a stone in 6 weeks is quite a lot.