Where should one send a tie to be professionally cleaned?
Although I have never used their service, it appears from a search of the online style forums that Tiecrafters is the consensus favorite. Their tie cleaning service is $10.50 per tie, with a four tie minimum.
By no means should you take a tie to your local dry cleaner. Your neighborhood cleaner is probably clueless about how to properly clean a tie. They would likely press the tie, causing the rolled edges to be cruelly flattened and possibily even damaging the silk.