As a girl 3DS gamer myself, I highly recommend some of the games suggested in this thread:

1) Style Savvy: Trendsetters - awesome fashion game, really addictive, loads of fun.
2) Rune Factory 4 - not-so-cutesy farming game (if Harvest Moon is for young teens, Rune Factory is for older teens with more detailed artwork and mechanics)
3) Fire Emblem Awakening - romance, romance everywhere
4) Tales of the Abyss - epic, moving plot, has its cute moments but quiet serious too
5) Professor Layton & the Miracle Mask - for quiet nights