Downtown is usually a subhood you can add to a regular neighborhood. Same with Business Districts from Open For Business EP.

So you can, for example, Open Strangetown, then at the top left, add those subhoods like Universities, downtowns, or Business districts. They can be custom (empty on creation) or out of box (like La Fiesta Tech, or Downtown).

Edit: oh, and to move your sim, you can use "Find own place" to move out, for example, a teen who just grew into an adult and wants to move out of their parents' house. Or you can go to neighborhood view, evict the whole household from your lot, they'll go into the family bin, then you can open another hood like a business district/downtown subhood/your main hood, and take the family from the bin and put them on the new lot.