How do I get the option to purchase Proudspire Manor to show up. I read I have to do some Misc Quests for the Jarl of Solitude, but she hasn't given me anything.

Do the quests Falk Fire-breath/beard. Her little nord person thats always by her side in the castle. Eventually she'll give you a quest to put something in some location. ;3 Then you should [don't quote me] have the option to buy the house.

Might want ask this question in the hints section. You'll probably get a much better answer than this;

Help everyone you can in Solitude. That's how I got my home in Riften. I helped any townsfolk that needed it.