Saw this question unanswered on Reddit. Avrich's The Haymarket Tragedy puts this congress (Oct. 14–16, 1883) in an evening reception in Allegheny City's Turner Hall the night before, but doesn't appear to say where the congress itself was held. Where was it in Pittsburgh?
The Congress seems to have been held over 5 days. Sessions on the first two days were held at Allegheny City's Turner Hall, after which they moved to Brookman's Hall on Fifth Avenue in Pittsburgh.
The report on page 5 of the Pittsburgh Commercial Gazette of 13 October 1883 states the following:
The program as laid down now, provides for a session of five days, two of which will be spent in Allegheny and three in Pittsburgh. This evening the local organizations will receive the visitors and entertain them in Turner Hall, Allegheny. There will be a concert, and address of welcome and speeches by the delegates. Herr Most is expected to arrive to-day, and is down for one of this evening's speeches. Tomorrow morning at 9 o'clock the convention will be formally opened in the same hall. The morning session will be consumed in organizing the convention, examining the credentials and other routine work. In the afternoon a public mass meeting will be held at which speeches will be delivered in English and German. The evening will be spent in social intercourse, and on Monday the convention will be transplanted to Brookman's Hall on Fifth Avenue, and its work will commence in earnest. So far as could be learned there is no particular business to come up, but the condition of the workingman and all that pertains to his interest will be considered.
The Pittsburgh Commercial Gazette of 15 Oct 1883 contains a report on the first two days in Allegheny, including the text of what has become known as the Pittsburgh Proclamation or Pittsburgh Manifesto.
Further reports on sessions at Brookman's Hall were reported on page 5 of the Pittsburgh Commercial Gazette on 17 October