First, Kith will ask her if they have any knowledge on death . . . waitforit . . . cults. Death cults. The church likely just deals in their churchy things, but they may have some information about creepy, necromantic things. She says death is the natural order of things, so things that defy death ought to be on their radar. And if it isn't, then what kind of establishment is this?! Kith will just be irritated.
Since it's midday, I'm also alright with hanging out and leaving in the morning. If that's the case though, Kith would like to ask around for a library to do some necromancy cult research. She's pretty stuck on that (totally not real life breebles' fascination with cults seeping through).
If asked his opinion, Ch'dau will argue for getting the party rested and heading out in the evening as opposed to waiting for morning. Given that these undead seem more active at night, it makes sense to venture off in search of them at that time.