There are few finer feelings when in a strange city than walking into the lobby of a hotel that’s so loved and lived in, it’s part of the city’s timeline. When it’s the original Waldorf Astoria – fresh from an eight-year, $US2 billion ($2.84 billion) total refurbishment – you might have to sink into a velvet armchair in fabled Peacock Alley and realise you just checked into one of New York’s most famous hotels. Peacock Alley and Cole Porter’s piano. The “alley” – more like an exceptional lounge room with its distinctive fish-motif carpet in oceanic blue, and a boulevard-style entrance – is named after the promenade that once connected the Waldorf and Astoria hotels, and was the city’s place to strut. Today, you can sit at the mahogany art-case grand piano once used by former hotel resident Cole Porter, now part of Peacock Alley. This 1907 Steinway & Sons piano (on which he composed I’ve Got You Under My Skin ) still features the many ring marks from his Martini glasses.…