Squats are a classic for strengthening the quadriceps. Goblet squats involve small, portable weights that are often more accessible to a TKD school. They are also appropriate for strengthening younger athletes who are still growing, since they are not a maximal weight and are therefore unlikely to stunt growth.
Hold a kettlebell or whatever weight you choose and set your feet at just about hip width. Keep the knees squeezed out to angle over the feet without tipping inwards. Fold at ankles, knees, and hips to squat, not allowing the knees to pass beyond the toes.