You're still technically dragonborn.
If you get Hearthfire, eventually the Jarl of Falkreath will contact you, go from there.
That's the easiest way, I think.
Others will probably tell you the rest.
Ciao.
*Update*
I can't remember which, but winning the war on a specific side will banish the original Jarl of Falkreath from Falkreath and replace him with someone else. If this happens after receiving the letter, I do not believe it is possible to purchase land there any more. Be careful.
If you choose not to do the main quest, you will only miss out on the house (and becoming Thane) in Whiterun. The Hearthfire homes and thane quests for the other holds are separate. You just need to make sure that you have enough gold available.
Are you using the vanilla start, i.e. Helgen and everything? If so, I believe you should be able to do the quests that entitle you to buy a house in any of the other Holds beside Whiterun, which includes the ones in Hearthfire. Falkreath (Hearthfire) is usually the most straightforward to get, because the Jarl's task is usually 'go and kill some bandits', and then you just have to help three local citizens, several of them have tasks that are no more complicated than 'take this to that other guy in town'. Siddgeir's an ass, but he's a pushover, so.
If you're using an alt start mod, then I think it varies, but for example Skyrim Unbound you can save up 10,000 gold and buy Breezehome and become Thane of Whiterun, get Lydia as Housecarl etc, whether or not you are playing as the Dragonborn (if you have never used Skyrim Unbound, it lets you switch off dragon soul absorption and word walls altogether so you aren't the Dragonborn, or you can enable them at a later point.)
Except for Breezehome/Whiterun, the house in Windhelm is the only one not available, since it's only up for sale if you do the civil war, and you can't progress far enough in civil war questline without being revealed as the Dragonborn.
There are also a few other possibilites, depending on how much space you need: You could marry someone with a house. You could check out http://uesp.net/wiki/Category:Skyrim-Places-Safe and take your pick. And of course, if you're on PC, there are plenty of housing mods on Nexus.
I hadn't thought of that...
(It applies to my post as well in that he cannot possibly complete the war on either side.)
OP-if you are on PC then there are mods that let you play Skyrim as a regular person (ie NOT Dragonborn) and buy the house in Whiterun, etc.
Perhaps if you seperated the text into paragraphs people would be more inclinded to read it.
Because a long wall of text doesn't look particularly inviting regardless of what it is, just a suggestion.
Agree 100% and I DID NOT read that bloated paragraph.
I had a bit of a squint at it and it seemed like it had potential but then my eyes burned out and now I have no eyes YOU OWE ME SOME EYES, INTERNET.
Sorry, I'm a bit tired and silly.
I think people would be more inclined to read it if you'd edit it to split it up into paragraphs. Just a friendly suggestion.
Thank you.