It looks like the metal carcass is ready to start showing..
You only have 2 wheels so keep the tyres in the best, safest condition you can. If the steel belt looks like it might be going to show then buy a set of new tyres and be safe. Last of all by the looks of the wear and cupping you need to keep an eye on your tyre pressures or maybe the rear shock is stuffed. But my money would be tyre pressure.
If you're not planning a long trip, I'd wait until you see cord...unless it's just a chore to ride, then change it...actually change the front too in that case.