The place is Koma in Hidaka, Saitama. For a little over an hour from Ikebukuro (take the Seibu Ikebukuro line to Hanno, then transfer to the Seibu Chichibu line and get off at Koma Station), you will step out into fresh air, mountains, rivers, rice fields, and a lovely organic vegetarian cafe.
But first, Mt. Hiwada. This mountain is an ideal nature retreat for the impulsive. You don't need to get hiking gear from Montbell to climb this mountain, although you will see many people geared up like they bought every single item on display at the outdoor store. In fact, there is a proper toilet and a vending machine at the base of the mountain for those who decided to hike up spur of the moment. There are many ways to get to the top of Mt. Hiwada but the properly marked ones are called Onnazaka (female route) and Otokozaka (male route). Political incorrectness aside, you can guess which one is the easy and which one is the more challenging route. I have seen a woman in a business suit and 3-inch high heels go up the female route (really, you don't need specialized hiking gear). If you are up to a wall-climbing sort of challenge, I highly recommend the male route which is steeper but still scalable for three year olds (at least my kids could do it when they were 3). It takes about 30 minutes to reach the first viewing point, where you will be rewarded with a bird's eye view of Kinchakuda, the purse shaped field outlined by the Koma River. On a clear day, you might be able to see Mt. Fuji to your right.
Most people stop at this gorgeous viewing point to have their boxed lunch. But if you find this too easy, there is a higher peak to get to for another 10 minute effort. This higher viewing point gives a view of the city of Hidaka.
My kids and I usually hike up the male route and go down the female route.
From Koma Station, the foot of Mt. Hiwada is about a 15-20 minute walk.