I went there last year and had a lot of fun but my trip was half business/half leisure, less than a week and I'm not really a party guy so I probably can't give you a lot of advice.
I mostly moved around in subway which was cheap and very easy to use. You can download an app where you enter your starting point and destination and it will tell you exactly which line you should take and where you need to change (in case you need to).
As in most places, knowing some of the local language is always welcome. Most people were really happy with us just saying stuff like hi and thank you in Korean. With that said, all touristic attractions (that I went to) have information in english and most places we went to eat (even smaller/cheap ones) had english menus.
As for food. Honestly, everything I tried was good. From the korean BBQ to the filled chicken to the dumplings to the ramen equivalent. As everywhere there's different prices depending on how fancy you want to eat, though from my experience in the more expensive places you are mostly just paying for the place to look nicer but the food isn't necessarily better. The one thing that was a bit of a letdown was the ice cream, had heard a lot about korean icea cream but it's pretty meh, sometimes they'll present it in an original way but the actual ice cream itself is nothing special.
When it comes to drinking, alcohol was pretty expensive so we mostly drank a lot of soju which is the local distilled beverage. Reminded me of Sake but I liked the softer flavor of this one better (they also mix it with beer which is pretty good)
As for places I went to a lot of museums. Most of them are really interesting and well made and I was surprised by the fact most of them are either really cheap or free. Having been a bunch of times in Europe where they charge you $10 for every tiny thing I was pleasantly surprised.
Gyeongbokgung is awesome (kinda hard to miss though since it's giant and centric). I'd recommend looking up the hours of the oficial free guided tours of the palace which are pretty good and will give you a deeper appreciation of the place
Seoul tower is fun for a nice view of the city, you can go up with a cable car (or you can walk, it's not very long). It's nothing spectacular if you have been to to other similar places but, again, it gives you a view of the whole city. I was there in winter so the surrounding park was pretty dead but when it's all green it must be much nicer:
The war museum is totally worth a visit. It has an entire floor dedicated to the korean war and then another one for more historical conflicts. It just really well made and interesting, they even show movies and there's some short "4D" experiences. It also has an exterior section with a bunch of war vehicles you can check out:
Under this statue in Gwanghwamun Plaza there's another museum about the creation of the korean language as well as a legendary naval captain (general). Also worth checking out
. Learning basic Korean words and phrases would be smart, but anything else that helps?
