When you first reach Whiterun, you’re given a chance to view a conversation between Adrianne Avenicci and one of the various Battle-Borns that wander around the city. This is a good opportunity to talk to the less-famed blacksmith of Whiterun, who not only supplies herself but also Uferth War-Bear, who waits inside her shop. You can find out from her, by inquiring of her skill, that she has just finished her best work- a greatsword that she wants given to Jarl Balgruuf. Since you can’t give it to him, she wants you to bring it to her father- the Jarl’s advisor Proventus Avenicci.
When you get into Dragon’sreach, you get your chance to pass Proventus the sword and pick up 20 gold for your trouble. You can also talk to Farengar about any other wizards in town- he will be reminded that he has some Frost Salts that need to reach the local alchemist, Arcadia. Tote those back down to Arcadia’s Cauldron, the alchemical shop off the city’s main square. The healer will give you a Potion of Brief Invisibility, a Potion of Enhanced Stamina, and a Potion of Illusion.
She will also count herself as your friend, which oddly gives you the freedom to take most of her display wares with no issue. If you -are- of a larcenous bent, though, be aware that these materials will be returned as though stolen if you find yourself paying a fine while carrying them- but they won’t reappear in her shop. Oops.
While you’re out and about, you’ll probably see a few interesting people and/or conversations. Brenuin, the local beggar, will reply to inquiries if he’s thirsty with a request that you steal the bottle of Argonian Ale found in the kitchen of the Bannered Mare. If you’re inclined- or you really need a Potion of Vigorous Healing, then you can accept. Should you succeed (a daunting task with the well-lit building and numerous people within, particularly Saadia’s penchant for walking into the kitchen at weird times) you can make this trade with him. Unless you have excellent timing, you should probably wait until you’ve got a rather high Sneak skill before attempting this.
Lars, the young boy of the Battle-Born clan, can be found in the rich district getting bullied by Braith, another local child. If you talk to him a few times afterwards, he’ll mention that he’s tired of being bullied, and offers you his entire life savings (two gold) to do something about the problem. Go talk to Braith, make any kind of threat you like, and she’ll give in, insisting that she just wants him to kiss her. Return to Lars or don’t- he’ll give you two septims next time he sees you.
Ysolda, who meanders around wearing a blue dress and provides you with Speech training if you like, wants to prove herself a good enough trader to buy and keep the Bannered Mare inn- but to do so, she needs to trade with the Khajit caravan. The Khajit she’s spoken to wants a mammoth tusk for the trouble, so steal, hunt, or find one and bring it to her for a rank of Speechcraft and a little gold. Also, it’s nice to hear her say ‘It’s a fine day with you around.’
Lastly, Andurs, the priest in the Hall of the Dead, has misplaced his amulet in the catacombs and needs it back- but several of the dead there have become restless, and he is just an old man. Enter and handle the three warrior skeletons so that you can scour the place- his amulet is downstairs in the small room found there, but you can also pick up a rare book, a potion, some skulls, and a few other miscellaneous things if you like.