Disclosure: I received complimentary products to facilitate this post. All opinions are my own.
I recently gave my daughter the game Niya for her birthday. It's a really unique game from Blue Orange Games - a company that I love. Blue Orange makes games that are fun and also encourage critical thinking and strategy, with games that appeal to young and old at the same time. Niya is no different. My daughter just turned seven, and is able to grasp the basic game play. She also loves the Japanese art.
Even though I'm more able to see the strategy, and often win, she is clever enough to manage to beat me occasionally too. A game only takes about 10-15 minutes, so it's not longer than her attention span, or too long for her sister to wait for us to play.
You can find Niya - and other Blue Orange games - at a variety of specialty game shops and bookstores.