It is a nice place, as long as you don't go TOO casual or sloppy,, you'll be fine. No swimwear, sweats, short shorts ... From the website: Casual attire is welcomed and appropriate
Tacky dressers: Ts, flip flops, gym wear should feel out of place, if they have ANY decorum whatever. The classic beauty of the Palmer House lobby should speak volumes to any diner. 🍽️
I've seen tacky people wear flannel and jerseys in there, so I assume they don't care how you dress.
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