Veggie Bite at 1300 N Milwaukee has really good fries. They're a vegan fast food place. You can even get them made up to be "chili cheese" fries, which are AWESOME.
Not quite a hot dog stand, but you can get a "hot dog" and fries there, and it's actually pretty good! But I'm a vegetarian, so I might have a skewed view of their offerings. =)
Another vote for Jude and Gene's on River Road near Grand. Also I remember Parky's. Demon Dogs at the Fullerton el stop were good- Are they still there?
My favorite chicago food joint has got to be Portillo's.. Am I crazy? can't beat the beefs (reg, big, or beef-n-cheddar), the bacon cheeseburgers, or the cheese fries!!! The Dogs are great there... My wife says the chop salad is the best...
Tamales
Ribs
and they serve beer too!!
Finish it all off with a chocolate cake shake..... Thats a meal!!
There is no better place for french fries than Portillo's. Their hot dogs are good, beef is fantastic, and burgers are just out of this world! Oh, and make sure to add some melted cheese to whatever for an even more delicious taste.