Exploring the length of Japan in a month is a serious option - I walked the 3200km from the southern tip of Kyūshū to the northern tip of Hokkaidō in 99 days, so surely you can do it on trains in a month!

Purchase a 21-day JR Pass and do some planning - this is just a sample itinerary - adjust it to what you’re interested in:-

Days 1-3: Do some exploring in Tōkyō.

Days 4-6: Catch a flight to Wakkanai at the northern tip of Hokkaidō; take a ferry out to the isolted island of Rishiri, climb Rishiri-zan on Day 5, then ferry back to Wakkanai on the morning of Day 6. Activate your JR pass to start on this day - take a train to Asahikawa.

Day 7: Do a daytrip to Asahidake Onsen in Daisetsuzan National Park, climb Asahidake from the top of Asahidake Ropeway, then soak in an onsen; stay another night in Asahikawa.