Tanzawa mountains
I'm a big fan of the Tanzawa mountains. Along with the Okutama area they're the "big two" in mountain ranges easily accessible from Tokyo and suitable for beginner hikers. But while Okutama is known for a lot of foresty trails, you can get a great view of Mt Fuji from most of the mountains in Tanzawa if your luck is good.
Tanzawa is also a great candidate to visit in the colder months if you're not interested in snow mountains, since a lot of mountains further away start becoming inaccessible due to the snow. And since its also known for leeches in the summer season, I would actually recommend you visit it in the colder seasons if anything else. The colder weather means your chance of seeing Mt Fuji increases too.
I made it a goal to climb 7 of the most famous Tanzawa peaks for the 丹沢ハイカー (Tanzawa hiker) YAMAP badge , which I completed in 2023, so I'll be updating this page with those hike reports as I write them!