Preheat the oven to 450 degrees. Pulse the onion, parsley, cilantro, tarragon, 2 tablespoons dill, the walnuts and garlic in a food processor. Add 3 tablespoons olive oil, the vinegar, 2 teaspoons salt, and pepper to taste; pulse until smooth.
Stir half of the herb paste with the yogurt in a small bowl; cover and refrigerate.
Season the chicken inside and out with salt and pepper. Loosen the skin with your fingers; rub some of the remaining herb paste under the skin and the rest on the outside of the bird. Truss the chicken. Place in a roasting pan; roast until the skin turns golden, about 30 minutes.
Reduce the oven temperature to 375 degrees. Toss the tomatoes with the remaining 1 tablespoon olive oil in a bowl; season with salt and pepper. Baste the chicken with the drippings and add the tomatoes, cut-side down, to the pan. Continue roasting until a thermometer inserted in the thickest part of the thigh registers 155 degrees, about 1 hour. Season with salt and pepper; let the chicken rest 10 minutes before carving.
Arrange the chicken and tomatoes on a platter; sprinkle with the remaining 2 tablespoons dill. Serve with the yogurt sauce.