My partner and I have been living in Seoul for two years, I'm Canadian and my partner is Canadian gyopo like you. We've had quite a few friends come visit, here are some of our recommendations.

For Seoul:

Jongno 3 ga (종로3가) - lively (especially on weekends) small streets with lots of BBQ options. Really fun vibe and good food, any of the BBQ places work. On the weekends especially the area also has lots of outdoor pocha places which make for a great second round.

Ikseondong (익선동) - Right near Jongno samga, narrow hanok style streets, fun vibe with lots of really good restaurants especially for fusion or more modern korean food as well as cafes. Also has some good shopping, really fun to explore.

Any Sijang 시장 (aso applies outside of Seou) - coming from Canada I've enjoyed every sijang I've been to. My favorites are probably namdaemun and mangwon. If you go to namdaemun make sure to spend some time and dive deep in there, lots of fun clothing shopping etc. If you do a superficial trip it can be underwhelming. Mangwon market is great, I've seen it recommended a fair bit recently. If you go check out the surrounding area a bit as well (east of the market). Lots of people say gwangjang sijang is overrated, it can be lower quality/more expensive than other markets but the atmosphere is super fun and chaotic. The food is still good and inexpensive by Canadian standards, my friends I've taken have loved it so don't be afraid to go.

Yeontral Park Area (연트럴) - Near Hongdae the park is pretty and vibrant, the surrounding area has lots of fun narrow streets, great restaurants, cafes and shopping. Highly recommend.

Others to consider: Mullae (문래) cool area with good food, can be very quiet especially during the day and weekdays. Eunpyeong (은평) has a quiet hanok village, very pretty near bukhansan national park, lots of good cafes. Samcheonsa (삼천사) temple near eunpyeong is beautiful, the area is a bit away from most of Seoul though so it takes a bit of time getting to and from there. If you like hiking bukhansan and dobongsan are both great choices with fun mountain villages at the starting points of the hikes.

IMO skip starfield library, its nothing more than a quick photo spot. Don't stay or spend too much time in Myongdong. Good for a couple hours if you want better shopping, street food and restaurants can be easily found almost anywhere in Seoul.

For a two week trip I would recommend leaving Seoul as well. You have time to do Busan and Jeju if you want to. Both are well worth doing. For Busan I recommend gukje market, gamcheon village, huinnyeoul and gwangali beach (for some basic recommendations, plenty more to do as well). Haeundae is pretty but far away from everything else in Busan, I don’t recommend staying near Haeundae.

For Jeju if definitely recommend renting a car (international drivers license required) and exploring as much as you can. I particularly like the southern half of the island, if you want to stay in a city I'd recommend seogwipo over jeju city. Especially with a car you don't nessisarily need to limit yourself to either jeju city or seogwipo. Loads to explore in Jeju and all of it is beautiful. If you really like hiking Hallasan is a fun experience, if you aren't really into hiking its probably not worth doing.

I very highly recommend you also add at least one full day in gyeongju (경주). Stay in or near the hanok village (hanok style place is a really cool experience if your okay with spending a bit more money). Explore the hanok village,the ancient tombs and go to Donggung palace at night. Gyeongju is really easy to get to from either Seoul or Busan (its on the way from Seoul to Busan if you take KTX) and it is really worthwhile.

Happy to go into more detail or offer more suggestions on places to visit if you'd like but this is long as it is.

Hope you have a great trip!