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It seems that one of the other taverns hosting Convention delegates was the City Tavern. John Adams reputedly described it as the 'most genteel tavern in America.' Washington had stayed here while on campaign in early August 1777.
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George Washington: Diary
Friday 6th. Sat for Mr. Peale in the morning. Attended the Convention. Dined at the City Tavern with some members of Convention and spent the evening at my lodgings.