They land, after a very disorienting few seconds, in what looks like a very old, very fancy train station, with roaring green fireplaces along the walls with various robed figures entering and exiting the flames.
"That... is very cool," Joey admits.
"Isn't it just?" Professor Suliman says, leading him to a baggage handling area. "Just put your suitcase on that rune - good. Now, we'll need to Floo to Labrador for the next leg of the trip - just stand in front of the fireplace and clearly say 'Hopedale Station,' then step on in."
"And Thalia and I won't catch on fire? That's very important to me."
"No, no - make sure to keep the birdcage in front of you and your arms around it, but that's the only danger, there's a persistent Flame-Freezing Charm on the fire when it isn't Floo-capable."
"I have no idea what that means," Joey says, "but you seem to, and I think that's what matters."
"Indeed. Just follow my lead," she says, and walks up to the nearest fireplace and states "Hopedale station!" The flames flare green, and she steps through.
Joey steps up, shakes his head vigorously, says "Hopedale station!" and walks in.
It's less disorienting than the earlier teleportation was. He feels like he's falling, which he doesn't love, but it's not like he's being aggressively compressed, which he liked even less. After a while he lands, and stumbles out the other side, clutching a complaining Thalia.
Professor Suliman awaits him, and she beckons him after her. "From here we'll take a series of Portkeys," she says.
"Words, words, words," Thalia comments.
Portkeys turn out to be a class of small enchanted objects that teleport people with yet another entirely distinct unpleasant sensation. They take four of them, from Labrador to Greenland to Iceland to the Faroe Islands, from which Professor Suliman Apparates them (the squishy-uncomfortable kind of teleportation) to Scotland, then London. Specifically a bar, where she sits down, lays a silver coin on the counter, and orders something called Firewhiskey.
"Can I have some too?" Joey asks. Then the bartender pours some, and he smells it, and he wrinkles his nose. "Actually, never mind."
"It's intensely alcoholic," Professor Suliman explains, "which I currently want very badly, because I hate intercontinental travel." She downs the shot, shudders, and allows a trickle of steam to escape her ears and nose. "Much better. Do you have any shopping to do before we turn in for the night?"
"Time zones, mister Reed, wait for no man. It's 8:00 PM."
"Oh, disgusting," he says, making a face. "I'm not going to sleep in an hour."
"I have a phial of Sleeping Draught in my pocket that says you will!"
Joey makes another face. "Alright, I guess I'll do the rest of my shopping and then you can drug me. Can I let Thalia out of her carrying cage? She really prefers riding on my shoulder."
"As long as she prefers it enough that she'll stay there and not fly off, that's fine."