Temple stay near Seoul

I would like to do an overnight weekend temple stay not too far from Seoul. I will be in Seoul the preceding week for work and fly out at 5pm on the Sunday. Hwagyesa (basically in Seoul) and Jeondeungsa (on Ganghwado) look promising. Are there any others nearby? Does anyone have any advice? Would I be able to get from Jeondeungsa to ICN in time for my 5 o'clock flight if the program ends at noon?