A popular climb, but not only because it's one of the easier climbs in the area. The first pitch (5.9) is a little less than vertical and requires careful sequence planning making it an enjoyable puzzle. The second pitch (5.7) is a lower angle affair with great holds.
Conroy's Castle is really the southern end of the Forgotten Wall, so walking south along the base of the Forgotten Wall, you've arrived at Conroy's Castle when the climbing ceases to look like 5.11 or 5.12, and the cliff is curving around to face south. Charlotte's Web is left of the climb Clear Cut which is distinguished by having a fun-looking roof about 10m up.
8 or 9 quickdraws if doing it in two pitches, about 15 to link the pitches (which I would recommend). Bolted first and second pitch anchors. From the top of the second pitch double ropes would be required to rappel all the way to the ground, so use the first belay station as an intermediate rappel if on one rope.