groin injuries suck, because they kill your lateral movement. Walking hurts to because being bilateral, there is some sway left and right when we walk.
i might say for cardio, you could try the eliptical or bicycle.
As for weight training, you can go for machines instead of free weights, because they isolate muscles in the legs.
You can still work the core with abdominal excersizes, and upper body.
As for golf, if you hurt it swinging, i wouldn't take full swings. Chipping, depending on your pain level. Putting is good as well.