Actually, everywhere, though there are some caveats:
-Whiterun: Both getting the house and becoming thane are tied to MQ Dragon Rising. Thus, you need to avoid completing Dragon Rising to have the house without becoming thane. This can be done either by not killing the dragon, by not reporting to Balgruuf, or by moving away from him after getting MQ The Way of the Voice but before Balgruuf finishes his speech (which allows some continuation in the MQ.)
-Riften: Because of a timing bug, you have to do the personal quest (shutting down skooma dealers) and the five citizen quests (easy mode: Ivarstead is in the Rift,) or cause Maven Blackbriar to become jarl (see below,) before you can buy Honeyside. At the moment you buy it, another bug forces you to decide whether to become thane at that point, or to go to Honeyside and never become thane.
-Windhelm: Buying the house requires progress in the Civil War - in the Empire's case, completion.
-Markarth: If you do Molag Bal's daedric quest, he "gives" you the house that contains his shrine. Purchasing the real house requires level 20, and can become difficult if you get involved in the city's Forsworn drama.
-Riften and Markarth: Be aware that changing jarl will result in a short track to thaneship: you won't need to do the personal quest, nor the 5 citizen quests. Restoring the previous jarl (by changing it through MQ Season Unending and changing it back through the Civil War) will restore the added requirements. In Markarth's case, this will fix the problem that might crop up if you did Cidhna Mine first.
I'm leaning towards the house in Riften. I'm a mage from Winterhold and have no interest in the TG. I've no interest in politics at all- yet. It seems the easiest path without invoking the CW or main quest lines.