There are two bus stations in Korat, the smaller one is the old one and is close to the Yamo monument in the center. The one you want to be delivered to is the other one, newer and bigger, which is called "Bus station 2" by the locals or "Bor cor sor song" in Thai should get you to the right place.
This is the one that you'll probably be taken to automatically anyhow from Khon Kaen but if, by some chance, you end up at a small bus station then you are at the wrong one. Take a tuk-tuk ride to the other.
Steve G is right about there being buses everyday to Hua Hin. As you enter the bigger bus station then you need to go to the left hand side of the station, that's where the buses to HH/Pattaya/Rayong/Bangkok etc are in a long strip running up the left hand side of the station grounds. Going further into Isaan in generally at the front of the station.
