I would like to travel to HH for some days, I am coming from Korat and I can stop at Don Muang airport and Mo Chit bus station. Do both places have buses to

Hua Hin??? Thanks

I think there is direct bus service between Korat and Hua Hin. In my many waits at the Hua Hin "tour bus" station on Petchkasem Road near Soi 62, I've seen big buses stopping there to pick up passengers and they have "Korat" in big letters/characters on them. However, I have no idea what the name of the bus line(s) is/are.

There is buses from Korat to Hua Hin

http://www.thailand-huahin.com/huahin-chiangmai-korat-bus-timetables.html

If you don't want to use that bus I don't think Don Muang runs buses to HH, and i'm pretty sure Mo Chit doesn't either

Swampy Airport do run buses to HH

The big buses to HH run from Sai Tai Mai Station which is far out from Central BKK and you would need to get a Taxi there

You could get to Mo Chit and then get the BTS to Victory Monument and get a minibus from there, the minibuses are directly under VM BTS station, travelling time is around 3 hours

Khorat HH exists indeed.