Flights with KE or OZ are the same price, Weekday flights are the cheapest, (Mon to Thu) are about US$65 each way, Fri-Sat-Sun are about $75 each way.
If you fly with KE you can fly business class for about $20 more each way. This will get you lounge access in GMP- free broadband internet computers, drinks and snacks.

There is no meal or snack service on any Korean (KE/OZ) domestic flight, in any class.

The flight from GMP takes 1h05m, and if you leave from PUS, it is about 45min, and a little cheaper.

There are international layout flights some of the day, and some domestic lay out. If you fly on the 777 or A330 with KE it will have the international F cabin (58" and 62" pitch), then J (50" and 45" pitch) and Y (33-34"). Pay for business class, and you may end up with the F seat- as for the front row at C/I. Domestic business has between 38 and 40" with 737's (500,800,900) and A300. The Y pitch varies from a tight 29" to 32". Ask for the exit row, they often are empty!

We went to Jeju 4 years ago, for 5 days, in winter. Nice snow on Mt Halla, just after the snow festival finished, but it was still set up.

I hear that the Hyatt is nice there, though we stayed at a local place, as we had booked a few days before Chinese NY, and were lucky to get anything!