In the age of google search and Alexa answering our every question or command, I believe we can still encourage our daughters to stay curious and use their imaginations.
I believe there are 3 ways that inspire lifelong learning:
...triggers their imagination, creating other worlds in their minds, giving them access to others' personalities and lives, describing new places or even history. (and obviously so many more things that would take a lifetime to talk about)
Give them some ownership at the library, have them take their own bag, and let them pick out some books they think look interesting (within reason-you are the parent).
BONUS: Go on a "coffee" date. Head to your local coffee shop with your library selections and read while enjoying a special drink.
...can be an unstructured and active task that helps them learn to make mistakes, process information in a tangible way, and allow them to create something physical from their own imaginations.
Creative play can be as unstructured as you want. Get your kids outside and see what they do when they get bored. They might run around the yard, draw with sidewalk chalk, or create a game. This could also be something indoors with some craft supplies, or a new cookie recipe and a free afternoon at home to hang out and see what gets created. They just need space and freedom to create.
BONUS: if you participate and have fun alongside your kids (if they want you to)
**I'll give you an example: my daughter was really into a tv show, they were having a marathon and part of it was a list of creative activities that the character does in the show. My daughter wanted me to do this with her, and it really wasn't something I wanted to do but I decided to join her and now even years later we still have those memories and even the crafts we made that make me think of my sweet girl I got to spend a special day with.
Gretchen Rubin does a good job of expressing this in her book Happier at Home, "Manual occupations such as gardening, woodworking, cooking,...knitting, can be deeply satisfying on many levels; the physical motion, the tangibility of the accomplishments, the pleasure of the tools, the sensory delights of the materials."
...I believe this one is so simple that we often miss it. Taking time to look at our surroundings, whether at home, in nature, or in a city. We can get inspired by looking at colors, textures, architecture, smells, light, or even people watching (no judging here, just appreciating all the differences).
Invite them to go for a walk in the park with you and ask them to notice 3 new things that they never noticed before, maybe even collect a few leaves or rocks along the way.
BONUS: take a sketchbook and some colored pencils (you'll need something to carry them in) and take a few minutes to sketch what you see
It may take some structuring time for your daughters if they aren't immediately interested. The point is for them to learn to love the process of learning, to have fun, to discover what they enjoy. Its an opportunity for you to give your daughter an acceptable amount of control over her life and allow you to connect with her at the same time (even if you aren't participating directly).
Every girl is different and will be interested in some of these tasks and others may not. They are not mutually exclusive. And even better when one (such as reading) sparks an idea for creating (writing, or drawing), or visiting a new place (observing) gives her inspiration to decorate her room (creative play). The possibilities are endless. Stay curious!