Absolutely, I'd be happy to help you plan a relaxed 25-day itinerary in Japan that includes parks and green spaces. Let's get started!

Day 1-5: Tokyo

• Day 1: Explore Shinjuku Gyoen National Garden and Yoyogi Park
• Day 2: Visit Ueno Park and Asakusa for a leisurely stroll
• Day 3: Discover the peaceful Hamarikyu Gardens and stroll around Odaiba
• Day 4: Spend the day at the beautiful Meiji Shrine and Harajuku's Cat Street
• Day 5: Relax in the serene Rikugien Garden and explore the trendy Nakameguro area

Day 6-9: Hakone

• Day 6: Travel to Hakone and relax in an onsen with views of Mount Fuji
• Day 7: Visit Hakone Open-Air Museum and enjoy a boat cruise on Lake Ashi
• Day 8: Explore the Hakone Botanical Garden of Wetlands and Hakone Gora Park
• Day 9: Relax in a traditional ryokan and enjoy the natural beauty of Hakone

Day 10-13: Kyoto

• Day 10: Visit the stunning Arashiyama Bamboo Grove and Tenryu-ji Temple
• Day 11: Explore the peaceful Philosopher's Path and Nanzen-ji Temple
• Day 12: Discover the beautiful gardens of Kinkaku-ji and Ryoan-ji
• Day 13: Relax in the tranquil Maruyama Park and Gion district

Day 14-17: Nara

• Day 14: Visit Nara Park to see the friendly deer and Todai-ji Temple
• Day 15: Explore Isuien Garden and Yoshikien Garden
• Day 16: Discover the serene beauty of Kasugayama Primeval Forest and Nara National Museum
• Day 17: Relax in the peaceful atmosphere of Nara's temples and gardens

Day 18-21: Hiroshima and Miyajima

• Day 18: Visit Hiroshima Peace Memorial Park and Shukkeien Garden
• Day 19: Explore Miyajima Island and its famous floating torii gate
• Day 20: Relax on the beaches of Miyajima and hike Mount Misen
• Day 21: Enjoy the tranquil atmosphere of Momijidani Park and Itsukushima Shrine

Day 22-25: Kanazawa and Takayama

• Day 22: Explore Kenrokuen Garden and Kanazawa Castle Park
• Day 23: Visit the peaceful Higashiyama District in Takayama
• Day 24: Discover the beauty of Shiroyama Park and Takayama Jinya
• Day 25: Relax in the traditional onsen town of Takayama before departing

This itinerary allows you to experience the natural beauty and tranquility of Japan at a relaxed pace. Enjoy your trip!