(And in the morning kiss goodbye and a teleport home, no need to do the Walk Or Flight of Not Shame But Potentially Awkward Social Repercussions.)
She looks after Men and keeps an eye out for useful things for them to do. She goes to the orc colony to double check that they don't do the Elf marriage thing; they don't, and she can reassure the small orcs about that. She works on her spell, aiming for the elegant version over the bird-cargo version. She visits Lúthien sometimes (finds it much easier not flirting with her under the revised circumstances of her sex life), and checks in on Brithombar a couple times and delivers letters to Mithrim and chats with people there. She hangs out with Dwarves because Dwarves are great, and eventually they should have word from the other kingdoms about whether they want teleporting courier service.
So Loki learns the locations of other Dwarf kingdoms, goes and says hi, and sees what they'll pay her to bop around with messages and smallish things.
Cool. Does she have to do anything complicated to keep it all in one bank?
So she accumulates money.
And she shows up at Thuringwethil's place.
"I am here to sound you out for one, although it'd be less of a one-time thing, don't know if you're up for that."
"That is not unreasonable. No, actually the problem is that if Maiar in general come after me with unsavory intentions I cannot on my own locate them. The shadowcatcher only helps to a point. So while I am wanted dead I kind of have to hang out near some Maia, and I have a place to do that but I do not know that it is the best nurturance for the budding civilization of Men, who are even less able than I am to defend themselves from high-powered invasion."