To prepare Avocado Relish: In a small bowl, combine bell pepper, onion, vinegar, sugar, salt and ground red pepper; gently stir in avocado.
Meanwhile, preheat a countertop or charcoal grill; cook hot dogs until hot and lightly browned, about 5 minutes (alternatively, cook over medium heat in a large skillet, turning once). Spread cut sides of buns with mustard. Place hot dogs in buns; spoon Avocado Relish on top.
Serve with tortilla chips, if desired.