“At the head of noisy streets.” The Hebrew is literally, “at the head of the noisy,” with noisy being an adjective, a substantive, which native Hebrew readers of the time would automatically fill in with “noisy places,” “noisy streets,” etc. The point is that Wisdom wants people to have the opportunity to hear her, so she goes where the people are, which then are the “noisy” places.
The reason the verse says at the “head” of noisy places is that it is making a reference to the city gate, which is the “head” of all the streets in the city. Although the large city of Jerusalem had several gates, that was unusual because Jerusalem was one of the largest cities in ancient Israel (Hazor was likely as large or larger). Most of the cities in Israel had only one gate (although sometimes the location of the city gates changed, as we see at the city of Dan, which had a Bronze Age gate on the east side, but a later gate on the south side). From the city gate, all the different major streets of the city would start and then wind their way through the city, branching into different alleyways, but the gate was the “head” of all the streets.
“where the city gates open.” The gate of the cities in Israel almost always opened to a large open area where people gathered to meet friends, get the news, conduct business and just hang out to see what was happening. In Greek towns, this happened more at the town center, the agora (Acts 17:17), but in the cities in Israel the city gate was where the elders sat and the people gathered.
In the biblical culture of the Old Testament it was the custom that the elders of a city would sit at the city gate (Gen. 19:1, 9; Deut. 21:19; 22:15; 25:7; Josh. 20:4; Ruth 4:11; 1 Sam. 4:18; Esther 2:19, 21; 3:2; Lam. 5:14; Dan. 2:49; cp. Amos 5:10). Sometimes even the king of the land would sit at the gate of the city (2 Sam. 19:8; 1 Kings 22:10). Most cities had only one gate, and so everyone who went in or out of the city would have to pass through that gate. Furthermore, there was usually an open space just inside the gate so there was plenty of room for people to gather.
The elders at the gate were generally older, mature men who were the powerful men of the city. As elders and often acting as judges, they were supposed to be godly and wise, which is why “Wisdom” could be found at the city gates (cp. Prov. 1:20-21). However, it was sometimes the case that the powerful men of the city were self-centered or ungodly, in which case the advice they gave would be ungodly too. Proverbs, reflecting the wisdom of the time, advises people to get advice from a multitude of counselors, and often those wise counselors could be found at the city gate (Prov. 11:14; 15:22; 24:6).
The larger cities often had a “double gate” for security. A double gate was a gate complex consisting of an outer gate and an inner gate with a space between them. The idea behind the double gate was that if an enemy managed to break down the outer gate they would not be able to break down the inner gate because while they were trying to breach it the city defenders could shoot arrows and spears, or throw rocks, or pour boiling water or oil down on top of them from the city walls surrounding them. The Old Testament city of Lachish is a good example of that.
If the city had a double gate, sometimes the elders sat “in” the gate, in the shade between the walls. The Hebrew “in” can also usually be translated “at,” so whether the elders were “at” the gate or “in” it usually has to be determined from the archaeology of the city. For example, Bethlehem was not a big city so when it did have a wall during what archaeologists refer to as the First Temple Period, it would have been a simple wall with just one gate, not a double gate, so the elders would have sat “at” the gate, not “in” it. [For more information on the elders at the gate, and that a person could seek wise advice there, see commentary on Prov. 1:21, “at the head of noisy streets”].
Here in Proverbs 1:21, “Wisdom” is a personification; there is no “person” named wisdom, so what does it mean that she raises her voice in the noisy places? There were always older people and wise people with whom one could confer at the city gates and where people gathered.
The idea of the elders and judges of a city being present at the gate of the city is a consistent one through Scripture and the point Scripture is making is that there is no reason to be unwise about something, there are people who can give you wise advice if you seek them out.