Daejeon is about 1.5 million people. It's in Chungcheongnam-do, about 2 hours south of Seoul by bus or regular train. There are always tons of jobs availabe in Daejeon so finding work should not be too hard, though as always, finding good work takes time.
Daejeon is surronded on 3 sides by mountains. One of the sides is Gyeryongsan National Park which can be easily accessed by city bus within 45 minutes or less. It's a beautiful park with plenty of hiking opportunities.
The Foreign Scene: There are plenty of foreigners in Daejeon so if you need that foreign contact, just hop on down to one of the foreign bars.
Daejeon is large enough to have TGIF, Walmart, Outback, Carre-Four, Costco & Starbuck's but small enough to maintain a somewhat small-town feel. I definitely feel like i am in a small town after i return from Seoul.
IMO, Daejeon is a cool and relatively clean place to live. I've been here for 5 years and it's one of the few places I would consider living given what I want out of a city. I like having access to good cheese and tortillas but also like the feeling of it being a small city. There are also 2 micro-breweries.
Climbing Scene in Daejeon
Daejeon has one proper gym which i will be listing after the "new site" is up and running. It's a bouldering gym but big enough to not get bored to soon.
There are quite a few places to climb within 1 hour of Daejeon, not including hike-in time. Most of them are at Gyeryong National Park. I can think of 4 places off the top of my head at Gyeryongsan. Getting out to the park, as i mentioned, is easy and takes less than 45 minutes but the hike-in is usually at least 20 minutes long and sometimes 30-45 minutes long.
Daedunsan has some superb climbing but last i heard, it was closed to climbing.
You can also get up to Cheongju which has a few climbs and a climbing gym in less than an hour if you have a car.
The rock in most/all of Chungcheongnam-do is very brittle. You can get on some nice ganite but it's usually slab. But a lot of the non-slab climbing is on less than bomber rock, though it's not too sketchy. I wouldn't put a lot of trust in placing any gear here, though.
Most of the climbs are sport climbs or a little mixed climbing but I have yet to find a route in/around daejeon that is strictly trad.
IMO, i like sport climbing so if i have the day and transportation is not an issue, I'd rather just drive the extra hour and head down to Jeollabuk-do and climb at Halmae Bawi or Seonunsan. If I don't want to make a full day of it, heading to gyeryongsan will do in a pinch.
I have only ice climbed twice and both times have been at a short (10 meter) waterfall at Gyeryongsan. I have heard there is more to do there but I'm not sure the size nor the quality. Most ice climbers in daejeon head out of province to find good ice.
Hope that helps!