I thought I might as well chime in here - this thread has been lying dormant for the better part of five years!
The most prestigious hotels of the Gilded Age, then as now, were those established and run by Cesar Ritz. Having managed London's famous Savoy between 1889 and 1897, Ritz went on to open the first hotel to bear his name in Paris, on the swanky Place Vendome, in 1898. I'd go so far as to say that the Paris Ritz was the first truly 'grand hotel' in the same way that the 'Mauretania' and 'Lusitania' were the first true 'floating palaces'. Exquisitely decorated in the Louis XVI style - a far cry from the stuffy, over-upholstered look still so popular in the closing years of the nineteenth century - the hotel rapidly came a Parisian landmark, frequented by princes and millionaires alike. It is of no small credit to the staff of the Ritz that they were patronised by so tricky a customer as that legendary (and, in my opinion, insufferable) chronicler of the Belle Epoque, Marcel Proust. Then again, the doyenne of American literature, Edith Wharton, was distinctly sniffy about what she deemed to be the flashy international crowd who flocked to the Ritz and satirised it as the 'Nouveau Luxe' in her brilliant and savage novel of 1913, 'The Custom of the Country', and in several of her short stories.
I believe the John Jacob Astors spent their last night in Paris at the Ritz, before travelling to Cherbourg to board the 'Titanic'. Dorothy Gibson actually died there in early 1946!
Following the huge success of the Paris hotel, Ritz went on to open a sister branch in London in 1906. Situated by leafy Green Park on busy Piccadilly, the London Ritz was an immediate success and, even today, there is no one building so redolent of leisured and elegant Edwardian England. After a period of relative shabbiness in the 1970s and 1980s, the public rooms and private suites have been rejuvenated and revitalised and are now every bit as splendid as they were when the hotel first opened. The sumptuous Louis XVI decor - a symphony of rose-pink and gold - was carried out by the firm of Mewes and Davis who were also responsible for first-class interiors aboard the Hapag liner 'Imperator' of 1912 (subsequently the Cunard 'Berengaria') and the 'Aquitania' of 1914. The main dining room is perhaps the most beautiful in town!
As for other hotels...as Randy says, the Meurice and the Crillon in Paris were both absolutely top-notch - the Crillon in particular. It is here that the ultra-prestigious Debutante Ball is annually held. The super-elegant Plaza Athenee opened in 1911 and is now chicer than ever (a very demanding friend of mine won't stay anywhere else - not even at the Ritz - when she is in Paris). The venerable Bristol was also popular, particularly with older clients who preferred discretion to flash and sparkle. A Spanish branch of the Ritz opened in Madrid in 1910 - I imagine the Penascos would have been familiar with it.
In London, Claridges was a by-word for luxury and service - it is my personal favourite among the great hotels although the Art Deco interiors I so love were not fitted until the late 1920s and early 1930s. The sadly defunct Cecil was enormously popular with the Edwardian rich, as was the Savoy on the Strand - although this latter now survives mainly on a past reputation for greatness, which seems to have little to sustain it today. Brown's Hotel in Mayfair has been a quietly and discreetly grand venue since 1837 - it is name-checked in Wharton's 'Age of Innocence' so she must have approved! - and is currently enjoying something of a renaissance (beware the apple martinis!)
As mentioned above, the Adelphi in Liverpool opened around the time of the Great War and was, I think, intended to appeal to the same clientele who sailed first-class on the great Cunard liners. Although architecturally on a palatial scale, it has rather come down in the world in recent decades, so you'll have to use your imagination if you pay a visit today!