Okay. She... takes a bath, okay, and sees what there is in the way of clothes suspiciously already present in her size, since she didn't pack more than a couple outfits.

The clothes approximately fit, but aren't tailored exactly to her.

That's something! She dresses up nicely.

After a couple hours, there's a knock on her door. The woman is back to show her around town.

"I'm excited to see the sights! What-all is there?"

There's the market, a couple parks, an underground hot springs, the arena, the Royal Firebending Academy, and of course, the palace itself.

She will be happily toured about.

Her presentation is in the palace, tomorrow evening. They show her the hall where it will be, and ask if she requires any further preparations to be made.

"I'm not sure what I'm presenting or to whom or for how long!"

Her inventions, to a selection of nobles, generals, and sages. They would like to see each in action, and get an overview of the underlying principles. Was this not in the letter? She may have to speak with the scribes.

"It said that I'd be demonstrating them for the court, but not who the court consists of, or how much detail they'd want! Anyway, I'll need paper and ink if I'm going to be typing very much, cloth and thread if I'm going to be sewing much, wax cylinders if they want me to record something..."

All these things can be provided.

"Okay then!"

She's going to miss an installment of seed code to Eliko, isn't she, she doesn't want to inquire too conspicuously about how to send mail from here.

Probably.

She's escorted back to her villa, where dinner is waiting for her.

They're too kind. She eats dinner.

As darkness begins to fall, lampposts in the street flare to life. The city quiets as residents return to their homes and their beds.

She gets some sleep.

Her presentation isn't till the evening; she'd like to see if she can find a good library as long as she's in a big city.

There is a library. Unclear if it's a good one from outside. It seems to have a reasonable selection, at least. Her trip there is unhindered but not unobserved.

That's okay, she can just say she's a huge nerd about spirits.

The library has children's books in which spirits feature, but no serious scholarly treatises.

Oh well. She browses other sections. Chemistry?

Lots of work on combustion and exothermic reactions.

How stereotypical.

She browses most of the day and goes to collect her devices for the presentation in the evening.

Her escort's back. Would she like help carrying them?

Sure, why not.