I recently ran across the Slow Travel Web site and was immediately intrigued. The aim of the site is to encourage travelers to do their sightseeing at a slower pace by spending more time in one location before moving on to another. The authors recommend a stay of at least one week in a specific place, and provide a ton of information about accommodations for this kind of travel (e.g., villas, apartments, holiday cottages). The site offers predominantly European information, but there are also entries on vacation rentals in other parts of the world as well.
I can highly recommend this mode of travel, having experienced two weeks of living life like a Parisian (sixth floor walk-up and all) a few years ago. We rented an apartment in the 3rd Arrondissement, and enjoyed shopping at the local grocery store and getting to know our neighbors (it was hard not to, since the apartment faced a small central courtyard in the heat of summer). We had time to settle into the rhythm of the city, and didn’t feel rushed to see everything all at once (a good thing for introverts I think).