; Okay so after doing a lot of research, I found this PC.Click
It's split down the middle, meaning it should last you for a long time as is, but if you ever wanted to get into any bigger games, you can easily add an updated dedicated graphics card later on. (Plenty of youtube videos show you how, so don't fret. 5/10 difficulty level for plebs.)
I looked through the reviews and users who have purchased this have said they use a heavily modded Sims 3 game and it runs smoothly without a hiccup. Considering Sims 4 doesn't need as much beef as Sims 3, I'm hoping this is perfect for you.
League of Legends doesn't take much either. I used to play that on my potato from 2009. Hell, I even double checked the specs and the recommended graphics card is outdated and no longer sold, so you're golden.