After almost 2 years of playing, I realized that I have never actually lived outside of Whiterun, so I decided to move. Solitude was the obvious choice.

However, I can't seem to find anyone with a dialogue option for me to buy the home. Who do I talk to, and what (if anything) do I need to do to own a house in Solitude?

I still feel like a noob in this game...

You need to do the quest ''The Man who cried wolf'' and do Elisif's favor in order to buy Proudspire Manor.

The same as everywhere: you do jobs for the Jarl and after a while you'll be offered the possibility to buy a house in the city, before becoming a Thane.

Yeah Proudspire Manor is the BEST vanilla house in the game as well as the most expensive so make sure you have a minimum of 30,000 septims (Preferably more) to purchase and decorate it. The house is 25,000 septims alone and the fully furnished house (Along with the Hearthfire added children's room addition) is completely awesome. It will become your favorite quickly unless you just prefer cramped quarters.

Hjerim is not cramped, and personally I prefer it to Proudspire.

At least, you don't have to pay to get Proudspire cleaned of blood.

Much cheaper to pay for a bit of cleaning, than be taken to the cleaners buying Proudspire Manor.

Even then, you have to contend with the fact that Hjerim has been used by a necromancer.

As a rp'er, how can you live in a house that you can't cook in? Proudspire, unless you don't have the last 2 or 3 patches, has no cookpot thanks to one of those patches. Deal breaker for me. 3 characters own it and don't use it at all, the housecarl has it all to herself. I hope she's having fun. Hjerim or the HF homes for me thanks.

(Though actually, I just bought a great pc and started playing Skyrim on it this past Friday, so now I can fix stupid things like that. When I learn how! )