Get a random residential street name passing city, state?

There are lots of different things that have built within the OSM ecosystem, so I can't rule out the possibility entirely, but it seems unlikely that there are any existing tools that have been designed to return a random street. You'd probably have to come up with your own custom-built solution. One way to do this would be to get the boundary of the city, select a random set of coordinates within that area, and then query a reverse geocoder to get a street near those coordinates.