Shattered Weir is best location for this quest imo. Fastest way of getting there is to zone up to Tenebrous Tangle and then use the teleport to the Bonemire. You'll find yourself surrounded by the basilisks there.
Combine this city writ with the writ from the Concordium (stunning revelation) that also requires 20 basilisks.
Unfortunately, the other two factions don't have any city writs that involve basilisks.