It would be exceptionally easy to be here for years as an English teacher and not learn much Korean at all and still have a great experience. In fact, many people I've met do just that. Most important signs are in Korean and English. At work (especially if you work in a hagwon), I don't need to use Korean (and some foreign teachers are actually discouraged by their bosses from learning Korean so that they have to speak to the students in English only). Many Koreans speak a little (or a lot of) English and are quite friendly and helpful. The expat bars in Daegu are ridiculously easy to find (go downtown at night and ask a friendly looking foreigner where Thunderbird or Commune's is and you're halfway there), so you can make friends quickly. Gesturing will get you pretty far in shopkeeper interactions and other necessities.
Many people who live here but don't want to study the language argue that Korean is pretty useless in the global scheme of things (hence why the peninsula is crazy to learn English). I guess unless you plan to stay here a long time or become a CIA agent specializing in North Korea, I can see why that might seem to be the case. I don't know why exactly I took to studying Korean so quickly, but boy am I ever glad I did. If you are a foreigner in Korea and wondering if it's "worth the effort" to learn the language, I'm going to give you ten reasons why my answer is an unequivocal "YES!"
1. The phonetic alphabet is not too hard to learn and more regular than English's phonics (which are a hybrid of too many languages to be logical). Similarly the grammar rules, while dramatically different than English, seem a lot more consistent.
2. It makes me better at my job. I can see why my students make the mistakes they do and help them to overcome these obstacles. (Just as a note, I don't talk in Korean in my class much and if they know, or should know, how to say something in English I still make them say it in English, even if I understand the Korean).
3. You get compliments about your language skills frequently, even if undeserved. Good for the ego.
4. You can approach all those cute Korean guys (or girls if that's what you're into) with slightly more confidence. Seriously.
5. With all those vowel sounds, it's a great language to whine in--even better than French!
6. Studying deepens my relationships with the Korean friends I've made and helps me to understand the culture in new ways.
7. It makes daily life here that much less frustrating.
8. Learning languages makes you smarter. I'm pretty sure I read that somewhere, but I'm too lazy to research it right now.
9. It impresses the hell out of other westerners who have labelled the Asian languages "too difficult" (they aren't, they're just really, really different). That includes many expats you meet over here.
10. It's fun because it seems like you're writing in a secret code--like in high school when you were passing notes you didn't want other people to be able to read. I know that many people can read and understand it, but it feels secret and fun to me somehow. Like how my parents used to speak Spanish when they didn't want my siblings and I to understand what they were saying, until I started learning it from listening to them and they gave up. And sometimes it feels like I'm solving a logic puzzle.
Korean is hardly my first foreign language--I've had a smattering of Spanish (enough to read Pablo Neruda poetry and listen to Shakira's music with minimal dictionary consultation), French (all I've retained are basic greetings, random vocabulary, and the ability to translate cute t-shirts with The Little Prince on them), and Latin (which I studied for one summer intensively and remember declensions, word order, and famous quotes like Cogito ergo sum and Veni, vidi, vici). However, I've never made it to competency (a substantial step down from fluency, but still impressive) in any language before, but I think I'd like to try to do that in Korean.
Give it a shot, ne (yes)?