Good stretches for correcting posture?

Depends on what issues you have with your posture. If they're minor problems then the best way to correct it is simply to practice good posture.

Core should be engaged at all times. This might sound uncomfortable if you're not used to it but if you focus on keeping your abs tight it'll become second nature to you - I'd feel far more uncomfortable with my abs relaxed when I'm standing. Imagining there's a hook pulling up under your xyphoid process - the part where your sternum starts between your ribcage - helps to straighten everything up. Pull your elbows back slightly to get your shoulders in the right position. Look straight ahead.

Aside from that there's some general stuff you can do like loosening up your hip flexors and working on your thoracic extension; these may or may not help your posture but they're good things to get right on in any case.

It wouldn't hurt to do some planks, stretch out your hip flexors and strengthen your posterior chain. And practice good posture, of course.