I'll often hear the "slap, slap, slap" of her crawling off down the hall on her own, looking for an open room to investigate. Usually, I'll leave a couple of doors open for her, so she can play. Her favourite room is the bathroom, because it's almost always closed. When she's in there though, she goes straight for my makeup bag in the cabinet - at least someone is using it.
In the office, she can usually find some books close enough to the floor that she can reach them - or she starts playing with the 15 packages of crayons that I impulsively bought during the back to school sales.
In our bedroom, she usually just walks around the bed and tries to pull things off the nightstands.
And in her room she plays with the basket of stuffed animals on the floor, or opens her closet door to play in there.
I'll give her a couple of minutes to enjoy the independence of playing by herself, then I'll "go find her" to make sure she isn't getting into any trouble (playing with cords is one of her favourite games). She thinks it's hilarious when I walk in and say, "What are you doing?"
She's so funny. I love that she has that independent streak, even if it does drive me crazy.