Definitely Nancy Drew. Some good suggestions already, but I might also recommend:
Anne of Green Gables
The Little Princess
The Secret Garden
The Wizard of Oz (but I'm sure you've already thought of that one!
A Wrinkle in Time
Any of the Trixie Belden series
Rebecca of Sunnybrook Farm
Any of the Marguerite Henry books (I loved the Misty books)
Alice in Wonderland
That's all I can think of right now, but I'm sure more will come to me later.