I definitely move around. A part of playing for generations is discovering new gameplay, and I find I do that more if I move around, trying to really explore each world to the fullest before moving on. So far in my current save my sims has lived in Willow Creek (with Newcrest as a different part of town so moving freely between the two), Britechester, Glimmerbrook, Del Sol Valley, Selvadorada (very long "vacation" while exploring the joungle), Mt Komorebi, San Myshuno, Chestnut Ridge, and Oasis Springs and Strangerville (one family in each). They've also vacationed or lived temporarily in Windenburg, Tartosa, Sulani and Tomarang. So yes, they definitely move around and will keep doing so. I'm only on gen 3 at the moment, and have plans to explore the rest of the worlds in time.
