I just installed OSMand to try it out, and it didn't have the street I live on. It also didn't have my place of work on it, although it did have that street at least.

Seems worse than Google maps to me.

Did you also download the map for your area?

I downloaded the maps for my state. Are there local maps that I would need to download as well?

Open Street Maps have much more users (and thus better ground coverage) in Europe, e.g. Germany. I think that's why the experience may be diametrically different for different people.