I live in NYC also, and attend the Yankees games - I don't think the language is an issue (my kids are grown but went with me when younger). If you kept your kids from going places because they might be exposed to bad language they would have a pretty dull childhood.

Back to the restaurant topic, I don't believe it works to have one standard of behavior at an Applebees, and another at "better" restaurants. Children need consistency - how can a young child distingush between establishments enough to know that it's ok to act up a bit in one but not the other? It is appropriate to take children to family friendly places, and I believe they shouldn't experience fine dining until they comprehend and can adhere to acceptable table manners.