First, what ever you store them in needs to be archival material - aka acid free. If you contact art supply or museum supply stores (see link below for an example. Also has some very good advice). In general you want to keep the books out of sunlight, water, and bugs.

I have my children's books on my shelves, I don't want to stash them away unseen. However, they are away from windows, and are covered in Brodart plastic (archival acid free covers, found in many rare bookstores or comic book stores)

Here is a link that might be useful: the container store

Books, or any paper or textiles, should never be stored in the basement or attic. Heat, cold, humidity, insects, rodents...the list of book-destroying elements is long.

Children's books are often printed on cheaper paper than many adult books. I have a bookcase in the upstairs hall where I keep the books from my own childhood and my children's--the ones they have left here.

Best advice is to find space for a shelf or two or more in your living space and keep them there.

Thank you for the responses - I have so many books I ran out of shelving for them, so I am wondering what to do with the extra ones I still can't bear to part with -- I will keep the rest of them where they are, if that is the best case scenario. Thank you.

I've got my Hardy Boys books in a suitcase. Maybe I'd better check on those.

I agree that bookshelves in living space are the best place to store books, if space can be found. I keep my children's old books (and some from my own childhood as well) on shelves under the window ledge in the kitchen, next to the shelves where I keep my cookbook collection.