R.J.
I'm a big fan of NOT entertaining children. <Grinning> As in: that's not my job.
I should add, my son is NOT an independent child, but a social butterfly. Only at 8yo is he able to "go play" by himself for 15-30 minutes.
Anyhow... that aside. Boredom breeds creativity. And I have a life to lead. So kiddo would come along with me. Helping with chores, reading books, swimming, whatever I was doing he'd either help or do them with me. Of course I'd play with him, a lot, but I never* felt that my job was to keep him entertained.
* Ahem, I did until he was about 6 months old. And then I realized that I could either become a 1 woman TV set, or go about my life and have fun WITH him... or go back to work and put him in daycare. I chose to go about my life instead.