I have no idea what Sillim means in Korean but I believe it to be synonymous with booze and fornication.
I used to live in Sillim. I used to wake up and find cards with naked girls littered all over my front doorstep. On any given night, I'd roll into Sillim Station and see drunk people passed out in all bodily positions and girls wailing and crying hysterically over some useless asshole. Then I'd have to hopscotch over puddles of vomit (observation: Koreans eat alot of ramen) and walk past shame-faced, horny couples ducking into one of countless love motels in the area. And of course it would impolite if I didn't nod hello to the brood of pimps who stand at the same street corner every single night. In my beloved old neighborhood, you can literally stand there and inhale intoxication and sex. But however sketchy Sillim is, it doesn't have the red light district sleaziness of Itaewon.
In Sillim (especially over by exit 3 and 4), the streets are crammed with hofs, bars, restaurants, noraebangs, DVD rooms, and night clubs. It's where "real" Korean people come to party, vent, drink, and have fun. Everyone is friendly, genuine and WASTED. You won't find the slightest bit of pretentiousness here.
If I ever felt like a nice, long walk, I would stroll over to Boramae Park. It's a HUGE park and open whenever. During the summers, I remember stretching out on the grass at dawn watching the physically vigilant do laps around the track. Some nights, there would be light shows by the lake.
My favorite bar is Mong. It's intimate, they have real cocktails, and the food is yummy even if you're not completely sloshed. It's run by a family with the mother cooking in the back and the children up in the front running things. The owner, who goes by Justin, is so genuinely nice, and likes to play his favorite movies on a projection screen for some ambient entertainment.
Directions: Walk out of Exit 3, go straight til you see a Watson's. Turn right and walk until you see Mong which is written in Korean in orange letters on a black sign.