From the Clerk's Ward to the Hive, you have three possible avenues of entrance: Darkwell Court, Khaasta Row, New Tyr.
You, being by the former Hall of Records, are closest to the Darkwell Court Entrance (near the middle of the map). Here is what you know from your general Sigilian knowledge about each area:
Darkwell Court
The stretch of kips known as Darkwell Court lies between Whisper Way and Sandstone Row in the edge of the Hive closest to the Clerk’s Ward. This community and its peery-sounding name are home to the largest population of githzerai in Sigil, and true to form, the insular bashers have constructed a slice of their monastic society from Limbo within Sigil. None of the typical spiked, razorvine wrapped, bladed eaved kips common to the rest of Sigil. Instead, the homes are dull, flat-roofed, rarely over a single story high, and rounded in places. The wizened matriarch of the community, Divin Anesh controls everything within the tight-knit court, more or less, and those wishing to do much beyond simply walking through the court would do well to request to speak with her.
Khaasta Row
This small neighborhood, adjacent to Darkwell Court, is the home of a number of the reptilian Outlands species known as khaasta. The group, knowing full well their reputation among most Cagers as a race of mercenaries, barbarians, and raiders, rightly fears retribution from less than trusting neighbors. Faced with this local opinion they keep mainly to themselves and rarely bother others, especially the githzerai nearby, who at worst seem content with their neighbors who share the same “keep to themselves” attitude.
New Tyr
This small squat was settled by a number of bashers from a Prime world called Athas some years ago. The self-sufficient and tough bashers that call it home typify the area; they respect strength but seem mighty peery of wizards and gith of both varieties. In recent years, the residents have taken a great shine to the clerics of a number of Sigil’s major temples that have preached to the community in order to gather converts. The concept of deities who exist and answer prayers seems almost a novel concept to the Athasians, and a growing minority of them have converted to several of Sigil’s major faiths with gusto. Among the population, which is largely human, there are a number of half-giants, various genasi, and a number of odd human/dwarven half-breeds called muls by the locals. The citizens of New Tyr have attracted a large amount of attention from the Sodkillers for their seemingly inbred toughness, resilience, and work ethic. Thus far, however, the faction has had little success in persuading the Athasians to fall in any numbers towards their own philosophy.