After you leave the hotel, head for the train station (by clicking on the sign at the right that says, "Welcome -- Train Station").
Hint 2
In the train station, you'll find Alec, the guy who tried to catch the person who stole your suitcase, standing at the far end next to the lockers. Remember what he said he does for a living?
Hint 3
He's a skiptracer -- something between a private eye and a bounty hunter. That sounds like exactly what we need, so ask him to help you find Moira.
Hint 4
It'll take him a bit, so while you wait, go make some cookies, then come back and buy yourself some train tickets.
Keep checking for Alec; if you complete the first "eerie tone" task, he'll be here when you get back from Giffnock. Ask him about Moira, and he'll send you off to Bearsden.
Buy me a coffee