Hi loeny, and welcome to NRaas.

The answer to your question is...well, maybe kind of but with some limitations. TS3 doesn't have a concept of districts within the same world like TS4 does. Each neighborhood (town, world, they all mean the same thing to TS3) is self-contained and only one such can be the active focus of play at any given time. Nothing progresses in worlds other than the one currently being played in; it's as if everything in the not active worlds is frozen until you actually play there again. Sims in not active worlds can be set to age or not as an option, but that's just the number of recorded sim days they have been alive and is not really by itself any kind of progression. Also, for sims who are employed in any capacity, they must work in the world in which they live.

Each world has its own residents and typically has some version of a number of basic lots like City Hall, Grocery Store, Schools, Book Shop, Stadium, etc. None of those required exactly, but it might be kind of awkward to play in a non-WA world where sims can't buy groceries and books or go to school. Many of us do play systems of Traveler connected worlds within the same game, and each of those worlds can certainly have a character and flavor all its own once you get beyond the basics. And we have sims in each world who know and/or are related to each other, can visit and move (as in move to a new house in a new world) between them. But a sim can't really start in World A in the morning, have lunch in World B, see a movie in World C, and return home to World A at night because travel is expensive, jarring to the game system, and the day/time and all of the sims in World A would be exactly as they were when you left them upon your return.

As another example, if you travel your sim's kids to granny's (nothing wrong there, it's lots of fun to take trips like that) in World B on the first day of summer, the traveling party becomes your active household and you will be playing in World B. It will still be the first day of summer in World A when they return. You can't really leave them there and return back to play in World A without moving them into World B "permanently" first and then putting them into a frozen state as you shift back to play the parents.

But I think, with some creativity, you should be able to arrange a system of diverse connected by Traveler worlds to get many of the effects you were looking for within the limitations of what TS3 can do.

And, of course, in case you haven't seen this already:
<a href="http://nraas.wikispaces.com/Traveler+FA ... ler+FAQ</a> (especially the Switching Homeworlds section near the end)