In a large pot, cover the potatoes with water and bring to to a boil. Cook 25 to 30 minutes or just until tender; drain and cool. Cut the potatoes into quarters, and place them in a bowl.
Whisk together the vinegar, oil, dill, salt and pepper. Pour over the warm potatoes.
Stir in the chopped bell pepper, cucumber, and green onions; add cheese, and toss in to combine. Cover and chill at least 2 hours.