for my basement I made it my mermaid / underwater room, since the basement made more sense than any other room for
it
you could maybe make it a living room? lots of comfy chairs maybe a tv, fireplace, maybe one bookcase since you already have a library, some magazines, if you've got a 3ds or wii u you could put them in there?
my basement is like.. kinda like a studio i guess? i don't know what it would be professionally called but all my mannequins are in a corner with gracie outfits that i'd never wear and in the other corner are cameras and studio lights. rope partitions line my bottom walls and the other side has a bulletin board with a cubby/locker thing next to it. there's a sewing machine next to the mannequins to i guess look like the costumes they're wearing are sewn? i'm not good at explaining but yeah.
What is you did something similar to a library like a reading room? You could have a couple of bookcases and magazine racks, with tacks of magazines and books on tables or the floor, along with lots of pillows, chairs, tea/hot chocolate, etc. You could also just do a nice little cozy living room with a tv and some chairs, couch, and plants.
I made my basement into a restoration / pottery studio and decorated it with museum art, pots, etc. I made it into a crafty area but also a little messy like an actual basement. In my other character's houses I have a bar, a bathroom, and another bathroom I want to turn the bar into a speakeasy and have the back/bar part hidden by the large bookshelf.
I want to go for something a little darker in my basement. My town is going for a sort of emo, dark, night time feel so some creepy elements seem appropriate.
I'm thinking along the lines of a cult room with skeletons and candles in it. Maybe just me though.