Since it will cost you nothing to accept Cordelia's company and hear out her suggestions while you're in the planning phase of your quest for elemental offerings, you take her up on her offer - although you're careful to point out the limits of the help you can accept, without potentially weakening the value of your intended sacrifices. Cordelia responds to that with a single disdainful sniff, but agrees to heed the terms you lay out. Assistance with researching the history and reputation of the various holy spots you've identified is fine. Even following along when you go to visit a shrine or temple is okay, as long as Cordelia restrains herself to observing your hunt, rather than being an active participant. And if weird, dangerous stuff comes up, self-defense is perfectly acceptable - though where you'll be able to help defend Cordelia if needed, she won't be able to return the favor. That's a bit of a sticking point, until you admit that you're not overly inclined to go for the really high-value, potentially dangerous offerings.

With that settled, and Cordelia having ducked into her room to get dressed in the meantime, the two of you and Briar resume the research phase. Cordy's greater skill with computers speeds up your online search to some degree, and watching her work gives you an opportunity to make notes about how to better handle one of the machines. It's not a skill you've had much chance to hone: your folks could probably afford a computer, but they've never seen the need to get one; your computer classes at school have, to date, mostly been typing lessons on out-of-date machines that don't have internet connections; and you don't get over to Cordy's place very often. For all those reasons, as much as the usefulness of the information she's helping you locate, you pay close attention to what your friend does.

Gained Computer Literacy F
Gained Annotated Map

When the pangs of hunger begin to make themselves known, you call a halt to the research party. Cordelia has no objections to your suggestion to order room service, and neither does Lu-sensei when you wake him up at about five to six. Given the busy day you've already had and the full one you plan tomorrow, you don't skimp on your personal order, while your companions go with somewhat lighter meals.