Firstly make sure you have enough flash while you are there so you don't run out while out and about.
As for where to dump it at the end of each day... can you take a laptop with you? Check for free space before going of course. If necessary buy an external drive for more storage. Depending on how paranoid you are, consider making two copies of everything in case of any loss of damage.
Actually, Seoul has great internet access compared to the Western world. If you pick a place with a good broadband link (I got up to 60Mbit download speeds at my hotel!) then you might be able to make online backups too. I don't know where to upload them to though...
There are some downloading units, which typically contain a small HD and will allow dumping of flash into them directly. But I don't have any experience of these.
Oh, remember to bring a power adapter with you. I never managed to find out while I was there but luckily I took a universal one with me. The sockets in the hotel I stayed in took mainland Europe style plugs.
_________________Canon DSLRs: 7D2, 7D1, 5D2, 1D, 600D, 450D full spectrum, 300D IR mod
Lenses: EF 35/2, 85/1.8, 135/2+SF, 28-80 V, 70-300L, 100-400L, TS-E 24/3.5L, MP-E 65, EF-S 10-18, 15-85
3rd party: Zeiss 2/50 makro, Samyang 8mm fisheye, Sigma 50/1.4A, 150 macro, 120-300 f/2.8 OS
Compacts: Sony HX9V, Fuji X100.