-- Adrianne Avenicci: Miscellaneous Quest -- Craft an Iron Dagger
-- Adrianne Avenicci: Miscellaneous Quest -- Deliver the Sword to Preventus Avenicci
-- Aela or Ria of the Companions: Miscellaneous Quest -- Speak with the Leader of the Companions
-- Alik'r Warrior: Story Line Quest -- In My Time of Need
-- Amren the Redguard: Miscellaneous Quest -- Fine Amren's Family Sword inside White River Watch
-- Carlotta Valentia: Miscellaneous Quest -- Talk to Mikael about Carlotta
-- Danica Pure-Spring: Story Line Quest -- The Blessings of Nature
-- Farengar Secret-Fire: Miscellaneous Quest -- Give the Frost Salts to Arcadia
-- Farengar Secret-Fire: Miscellaneous Quest -- Use the Arcane Enchanter
-- Hulda the Innkeeper: Miscellaneous Quest -- Visit the Shrine of Azura
-- Jan Battle-Born: Miscellaneous Quest -- Speak with the Leader of the Companions
-- Mikael the Bard: Miscellaneous Quest -- Investigate the Bard's College
-- Proventus Avenicci: Miscellaneous Quest -- Kill the Bandit Leader located at Silent Moons Camp
-- Ysolda: Miscellaneous Quest -- Bring one Mammoth Tusk to Ysolda
-- Dragonsreach - The Legend of Red Eagle: Find Red Eagle's Sword (Miscellaneous)
-- Dragonsreach - Lost Legends of Skyrim: Forbidden Legend (Story Line Quest)
After you cross the bridge turn right and follow the road along the river until you reach another set of bridges, and you can see the city on the hill to the left in the distance. Find the road leading up to the city and follow it to discover the Whiterun Stables and, further on this winding path, the entrance gate to the city, which is presently closed.
When you are challenged by the guard, tell him that Riverwood seeks the Jarl's aid and you will then be admitted, so head through the gates and into town! Once inside, take your first left and follow this path to the stairs that lead up to the Dragonsreach -- which you discover upon arriving at its doors!
When you step through the gates the first building on the right is the smithy -- you can do a short Smith Training Quest that starts with making a Dagger by talking to Adrianne outside of the shop. You can sell any armor and weapons you have picked up to the counterman inside the Smithy -- and you should do that before you move along!
-- Visit the Bannered Mare Inn --
At the Inn you can flag a number of quests and even complete one you flag from Carlotta. Look for a female warrior named Uthgerd the Unbroken -- who has a story to tell you -- and who will fight a bar brawl with you for a 100 gold coin purse! You can easily beat her, and that makes it an easy 100 gold coins, so why not? If you beat her she will be willing to be your companion, and battle at your side out of respect for your skills as a warrior.
To add her as your companion simply tell her to Follow you -- consider doing that because having a fighting companion can really help you a lot!
If you flagged the Miscellaneous Quest "Kill the Bandit Leader at Halted Stream Camp" when you were in Riverwood, you may want to complete that before you head back to Riverwood to do the Bleak Falls Barrow Quest, since it is on the area of Whiterun... Also note that inside the Bandit Camp are some Mammoth Tusks that will allow you to complete the quest for Ysolda as well! Your call, but because of the massive gains it represents I chose to do it...
Meeting Your First Wizard
Welcome to Whiterun
-- Wizards and Enchantments --
Go inside Dragonsreach and seek out the Jarl, and once you tell him what you came to tell him you will complete the quest "Before the Storm" and flag a new quest, "Bleak Falls Barrow" in the process. Follow the Jarl to his wizard when he asks you to, and you will get a briefing from the wizard Farengar!
After you get your briefing take the time to ask him about enchantments, and for any other information that you think you want to know. Information is what you lack right now, so asking questions not only gets you that but you can also flag new quests in the process of asking questions -- like the Miscellaneous Quest to deliver frost salts to Arcadia and using the Arcane Enchanter to learn an enchantment from a weapon or other enchanted item (doing that destroys the item though).
-- Flagging Additional Quests and an Important Read --
Now BEFORE you do anything else, you need to head upstairs in the Jarl's Dragonsreach Palace and, making damn sure you do NOT draw your weapon, begin searching the bookshelves in the upper rooms. Note that I said READ, not STEAL.
(1) Find a book in a bookshelf called "Lost Legends" and read it to flag the Quest Forbidden Legend.
(2) On a table in a bedroom on the second floor of the Jarl's Quarters is a stack of two books - the top of which is called "The Legend of Red Eagle" -- read it to flag the Miscellaneous Quest to find Red Eagle's Sword. This is an IMPORTANT Quest even if it does say Miscellaneous!
-- Onward Through the Fog! --
Open the quests menu and select the quest for the frost salt from the Miscellaneous list, making it your active Miscellaneous Quest, and then remove the flag from the Main Quest and put it on Miscellaneous so that you can now follow the marker to the Alchemist, who rewards you with a few potions. You can get training in Alchemy here later if you want, and use her kit to make potions, but right now you lack the ingredients and the money, so it will have to wait!
You can now head down into the city and talk to people to flag Miscellaneous Quests if you would like to pick up some easy XP -- note that the Companions Circle series can be very rewarding and you can complete it before you head off to resume the story quests to boost your levels to 5 or above if you want to.
When you are ready go ahead and leave town to begin our next little adventure to obtain the Stone for the Wizard -- because we are going to need to level up a bit before we can go after the Red Eagle's sword.