I know that the second Council of Clermont was (of course) in Clermont, Auvergne but do we know where (in terms of venue) it was held? Which church, hall or public venue that Pope Urban II gave his speech that started the First Crusade?
The Second Council of Clermont met in the Basilica of Notre-Dame du Port, though at the time it wasn't a basilica yet. Most of the Council was spent dealing church matters inside the building, while laypeople congregated outside. Hence, when it was time to make his famous call to arms, Pope Urban II went out and addressed a large audience in an opening before the church.
The Council of Clermont met in the Basilica of Notre-Dame-du-Port, and began by renewing the Gregorian decrees against investiture, simony, and clerical marriage. Once more, prelates, monks and laity came in from all parts: accounts speak of people drawn to the town by the council may have been as high as 100,000. On Tuesday, the 27th of November, the pope came forth from the church and addressed the assembled multitudes.
Balk, Antti P. Saints & Sinners: An Account of Western Civilization. Thelema Publications, 2008.
This opening is probably where today's Place Delille is located.
But in Avit's century, the spot was still surrounded by forest, and later, when the trees disappeared, an enormous open space was left, now represented by the Place Delille. This was, no doubt, the extent of the ancient Druid sanctuary, and it was here that all the dukes, counts, barons, and knights of France assembled in 1095 to hear Pope Urban the Second proclaim the First Crusade.
Gostling, Frances M. Parkinson. Auvergne and its People. Macmillan Company, 1911.
Although the present structure only dates to the 1100s as Michael Seifert noted in the comments, this does not mean the church didn't exist in 1095. In fact, Notre-Dame du Port was originally founded in the sixth century. By the time of the council, Notre-Dame du Port was already a venerable old church that had been rebuilt or substantially restored several times.
The church was founded in the sixth century by Saint Avit, bishop of Clermont from 571 to 594. It escaped the ravages of the Saracens in 731, and although the city itself was burned by the soldiers of Pippin in 761, it seems to have remained intact until the middle of the ninth century when the building was destroyed or severely damaged by the Normans. In 862 Bishop Saint Signon began the restoration of the church which was completed in 866. This Carolingian structure is not ours, for in 915 the church of Saint Signon was in turn destroyed by a second Norman invasion which left the city in ruins. The reconstruction of the new church began at the end of the first half of the tenth century along with the other restorations carried out by Bishop Etienne II.
Hibbard, Benjamin Howard. An Iconographic Analysis of the Choir Capitals in the Church of Notre-Dame du Port in Clermont Ferrand. University of Wisconsin-Madison, 1952.
Despite the presence of a cathedral nearby, the smaller church appears to have been more religiously significant.
Thanks to its holy patroness and her miraculous statue, the little church of Notre Dame du Port, and not the cathedral which so far outranked it in station, size and title, was the hearthstone of the religious and civic life of Clermont.
The American Architect and Building News. James R. Osgood & Company, 1899
According to the account of Robert the Monk, the famous speech was given in an "open space", different from where the business of the council was conducted:
In the year 1095 of our Lord's Incarnation a great council was held in France; more precisely in the Auvergne, in the city known as Clermont. Pope Urban II attended this Council with the Bishops and Cardinals of Rome. ... Having dealt with the ecclesiastical business on the agenda, the Pope came out into an open space of some size, none of the buildings being large enough to contain all those present. He embarked upon this speech to all, aiming to win them over with every rhetorical persuasion at his command, and said:
Robert's account of Urban's speech follows. Robert claims that he was personally present at the Council; there is no particular reason to believe or disbelieve this statement. He wrote his chronicle in 1107, twelve years after the events took place, so it is entirely plausible that he was present and was recounting his own memories; it's also possible that he was relying on second-hand accounts.
The account of Fulcher of Chartres, who is more generally accepted to have been present, does not mention the precise location of the speech. Guibert de Nogent, who wrote a history of the First Crusade but was not present at the Council of Clermont, provides no further details either.
There are three other sources concerning this speech, but I have been unable to locate English translations of their complete texts online. According to Wikipedia, two of them (Urban's letter and the anonymous Gesta Francorum) do not discuss the circumstances or content of the speech in any great detail. It's possible that the account of Baldric of Dol contains some detail about the circumstances of the speech, but like Guibert he was not present at the Council.