Business Casual is a good guide.
There is a dress code but I don't think they are strict. We were dressed up (long dress , dress shirt and pants with nice shoes) and a family came in with blue jeans, nice shirts and I thought tennis shoes. Do go there, it is a lovely experience!
I wouldn't worry about it...the manager is a little shabby herself. Have fun. Lol
As you're about to have one of the best meals available in the city, I'd say it's fully worth a little sartorial effort. (And don't miss the Garlic Soup!)
I wore shorts and felt underdressed, but was welcomed anyway, so not strictly enforced.
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