When Jessica arrives at the front desk, the concierge is talking on the phone about a suit being cleaned for a Mr. George Kaplan in room 796. This is a nod to the Alfred Hitchcock 1959 film, Der unsichtbare Dritte (1959), starring Cary Grant and Eva Marie Saint.
The 2nd reference made by the concierge could be Kay Thompson, the lady who wrote "Eloise at the Plaza" and has a room decorated in pink. The concierge at the end of his call says the champagne will be pink, of course.
Early on, the concierge takes a call from "George Kaplan" in room 796 about sponging and pressing a suit. This is a reference to Der unsichtbare Dritte (1959), in which the fictional secret agent George Kaplan is staying in room 796 at the Plaza. "George Kaplan" never had a suit sponged and pressed at the Plaza, though. Cary Grant's Roger Thornhill did, at the hotel in Chicago, after the famous plane chase scene.
In any advertising for Nick's business (the side of his truck, his business card), there is no mention of any 21st century means of communication, such as a website URL or an email address, with only a telephone number listed on the card besides the business name.