I can't think of any neighborhood that has nothing but sage growing in it. You can go anywhere in the neighborhood, as long as you don't click one of the other lots, without "leaving your home lot." So, you can go all the way down the street to the lemon trees, all around the perimeter of the neighborhood where various things are growing, without ever "traveling" anywhere. And since you don't have Seasons, you don't have to worry about things not being in season.
Now, I don't actually know the rules, but I'm assuming you aren't allowed to travel away from your home lot, at least until certain conditions have been met. But generally, the "immediate vicinity" of your home lot is anywhere you can go, without bringing up a loading screen. You can go anywhere within your neighborhood, as long as you don't click another lot and choose to visit it, without bringing up a loading screen.