I moved to NYC a few months back from Texas and I've really been craving good chili cheese fries. For reference, I've always loved James Coney Island in Houston and Ben's Chili Bowl in DC, both of which use a cheese product rather than a real shredded cheese, so that is fine in this search, but real cheese is always great. I also love the queso waffle fries at Texicali Grill in Austin, which don't actually have chili on them but are so amazing they really don't need it.
I'm more picky about chili than I am about the cheese - it should not have beans and it should not be too meaty. Really, It shoujld be more like chili con carne meat sauce than traditional Texas chili. I also like some good spice.