For most of us who grew up in Chicago, a "Chicago Hot Dog" was synonymous with a Vienna hot dog. At one point they probably controlled 85% of the local Chicago market. Their competitors before Red Hot Chicago came on the scene in the early 80's I belive were Kosher Zion and David Berg (which as noted above is now owned by Vienna).
Having sampled Hot Dogs all over the US, there is still nothing that compares to a well made, natural casing, all beef, Chicago Style Hot Dog. Pinks, Grey's Papaya, Nathan's, etc. all have their fans, and are all good in their own different ways. A person growing up in NY, looks at a Chicago Dog in a different way. People from elsewhere wonder what the whole "no ketchup" deal is, why the neon relisg, etc.
Above all else the Dog must be well made. Not overcooked, not mushy or rubbery, proper snap in the casing, correct proportions of condiments and a properly steamed bun.
Grill it, steam it, boil it......each one brings out a little different nuance of flavor.
What exactly is the dislike for a Vienna Dog and what flavor profile are you looking for, maybe that will help point you in the right direction.