Traveling about with pads is no trouble 98% of the time. You may get an ornery bus driver on occasion, but other than you should be alright. If you roll out with a crew, you may have to take separate buses, especially during the spring and fall peak seasons. Have you ever seen a million people on a mountain? You will.
The bouldering areas in Seoul are accessible by public transit, and most crags are reachable by intercity bus/train/taxi or some combo thereof. I know some of the boulders in the Busan area are similar but the newer stuff requires wheels. The is stone everywhere here, literally. After a few members of the crew bought cars, the number of areas has blown up.
As for traveling, my friend flew my Moon Pad (standard size) over from America with no problems. Pads here are not scarce per se, but the selection is poor (Mad Pads and Metollius Stomp). The big Metollius is gettable if you ask around enough.
Quick but important question: what size are your feet? big climbing shoes can be impossible here (as in over size 10US, even 10 can be tough). Also generally, any brands other than 5.10 and Evolv (which are actually pretty cheap) are hella expensive, unless you find a deal.