Before The Storm (Imperial)
 The Road To Riverwood
Once you leave the cave at the start Alduin will fly overhead on his way towards some mountains in the distance. Hadvar will say its probably best if we split up although its better if you stick with him especially if you want to continue with the Main Questline.
Keep following Hadvar until you reach the Guardian Stones and there you can choose between the Mage Stone, the Thief Stone and the Warrior Stone picking one will make your skills increase 20% faster for the respective group of skills.
Keep following him until you reach Riverwood and he will lead you to his Uncles house where he expresses his surprise but graciously invites you into his home. Once inside Hadvar tells him the story and his uncle will offer you some gifts. I would recommend taking everything as what you don't need you can just sell at the Riverwood Trader he then asks you to talk to Jarl Balgruuf and warn him that a dragon is on the loose and Riverwood is defenceless.
 The Road To Whiterun
Travel to Whiterun now whenever you enter the city seek out Dragonsreach palace. It is very easy to spot and its on your compass anyway. When you enter you will be approached by Balgruuf's Housecarl, Irileth she will ask you why you are here and you can answer however you choose. Once you speak to Jarl Balgruuf choose whatever conversational tract you desire and he will ask you to help his court mage, Farengar Secret-Fire.