50mn train away from Shinjuku Station is Takao San, a mountain in Tokyo’s doorsteps. it is an easy hike, about 2 hours up, a lot of nature and peaceful moment. so it can end up being crowded but it remains a nice place.
Spring is nice, you avoid the heat in town, if you go in the morning, it is not that packed and the square close to the cable car has shops and cafes for a break
Taking the cable car also take you to a panorama, there is a cafe with terrace there that has barbecue in the late spring as well as beer garden
in the autumn, it is a scenic place to admire the autumn leaves so get ready for long queues, lots of people, packed trains. this is 95% Japanese tourism and not very known by foreigners (yet), I hope it stays like that