Jeju in Winter for Lunar New Year/Chinese New Year (Seolnal) 2017: Any tips?

Hello, everyone.
My parents are coming to Korea in a few weeks and we will be going to Jeju for Seolnal (Chinese New Year).

I have only been to Jeju for a work trip that lasted less than 24 hours, so I was looking for some tips of where to go, what to see, and where to eat.

Thanks in advance!

PS. So far, I'm doing pretty well with updating a lot in 2017, but I have to dial it back a bit, I think. Going to run out of content soon, maybe.

UPDATE: Here is our FINAL Itinerary

Travel tips:
  1. Buy your SIM card: Prepaid 4G/LTE Sim Card: Unlimited Data+Voice call+SMS (5/7/10/15/30 days)
  2. Get a great view of Seoul: Discount Seoul City Tour Bus Ticket
  3. Great Korean (traditional and modern) culture and cooking classes.
  4. Check out these great things to do in Jeju!
  5. Don't want to rent a car in Jeju? Check out this Hop On/Off Bus Tour of Jeju
  6. Don't want to rent a car in Jeju? Check out this Taxi Tour
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