Day 1:-
Sam/Grepha:
Sam's search for a hat proves fruitful, and after a short exchange of gold he's able to pick up don what can only be described as a magical sombrero.

Grepha's search proves less fruitful - finding one man among a city of thousands in just a day with little guidance seems a bet on random chance more than any active searching, and though there are a number of false starts, Gil's head does not pop up in her sight line.

Leaf:
The markets are filled with people, though most seem more desperate than eager. The wares on offer are difficult for Leaf to parse through but they nevertheless snag a few baubles of value. From what Leaf can tell they got away with their thefts.

Spoiler: Loot
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One necklace, worth ~25gp
One ring, worth ~50gp


Grok:
Grok's search for the missing assassin proves fruitless - similar to Grepha's hunt - and his attempt to speak to the assassins in captivity proves just as poor. As Scar indicated, you are not permitted to speak with them, and the Flaming Fist turn you away, brooking no negotiation attempt.

When he takes up position across from the Merchant's League compound he's struck by how quiet it is. Though there are the occasional person coming and going, it certainly seems far quieter than you would expect for a bustling hub of mercantile activity and a focal point of the city's economy. Small town taverns see more comers and goers than their building, at least during the time Grok's observation. Everyone he sees appears normal, though some of them have strange gaits.

When Grok goes drinking, he inevitably finds himself drawn into a drinking contest - one which he succeeds at handily, drinking multiple challengers under the table. For his efforts he gets a nights worth of drinks covered, 7 gold coins, and he hears a rumour that a mage - Ragefast - is holding a nymph captive in his home.

Caelyn/Anri:
Caelyn's search for fellow elves takes much of the day. Ultimately, Baldur's Gate is a human city of human gods, and when she finally does locate a place for the Seldarine it's no temple or chapel; it's barely even a shrine, tended by a single wizened old elf in a side room of their modest home on the outer edge of the city. Few elves, it seems, even come around here these days, instead trading their gods for those of the city - for Tymora, for Oghma, for Helm or any of the others that aren't 'elven'. The old elf listens carefully, and offers you a vial of moonwater for your troubles, but ultimately believes that if an elf is being plagued by such dreams that it is a matter for the gods. With the Time of Troubles still fresh in so many minds, he advises that perhaps the gods can't help you precisely because a god is doing this, though for what reason he can't begin to speculate.

For Anri, he offers a small tome of elven legends and stories, of heroes, villains, and gods all. It's well worn and clearly has been read many times, but "better in the hands of someone who needs to read it fresh, than someone who has read it a thousand times."

That done, you peruse the shops for some tools and a lock, and acquire both for the cost of 35gp and get to work on training, though a skill is not mastered in a day, and by the end of your first day it's still going to be some time before you're "proficient".

Senna:
The big city markets prove a confusing mess for Senna, with countless people shouting their wares, upselling everything, and speaking a haggling language that is thoroughly offputting for a gal from Candlekeep who had yet to properly step foot in a city before now. The myriad of options ends up hindering more than helping, and ultimately of the items she seeks she finds only the scrolls, and they look to be a touch overpriced at 400gp each. Not overly so, but still above what you might have hoped to pay.

Vala:
With a smile and a wave Vala disappears into the crowded streets to "press some leather", as she put it, though to what end remains to be seen. She doesn't return at the end of the first day, but she said she might be a while, so this is no great concern.