Haven't played much Bethesda stuff in a long time, but if I remember correctly, you can save yourself some time at the start of Skyrim if you get the dragon artifact from the end of that dungeon by Riverwood (the one where you're supposed to get the Golden Claw for the merchant, something-barrow I believe) before speaking to the wizard in Whiterun since you'll already have what you need for his quest anyway. Basically, just go there first and collect whatever you find near the end and then you can skip having to go back through it for the wizard.