You can use Incheon International Airport and take a bus or train to get to Daejeon.
Check this link.
For a more thorough explanation, please check these slides. (You might want to print it out and bring with you.)
* Hotel ICC ↔ KAIST by Taxi
Fare: about 5,000 KRW (about 4 USD). (We don't have a tipping culture in Korea.)
Estimated time: 10 minutes
ICC to KAIST: Please show the driver "카이스트로 가주세요."
(You can find a taxi stand in front of Hotel ICC.)
KAIST to ICC: Please show the driver "ICC호텔로 가주세요."
(We suggest you to ask one of the locals to call a taxi for you as the taxi stand may not be easy to find.)
* Hotel ICC ↔ KAIST by Bus
You can use a bus (number 121) on the main road, if you would prefer.