Like what evilerniex said, Hakone is close to Tokyo, since you will be visiting Tokyo next time, might well go places that is not easier to access (compare those typical few prefectures that ppl usually visit)
I been to Japan five times (3x Autumn, 1x Spring, 1x Winter), however I never really been to central Japan.
the distance to toyama from tokyo is only 2 hrs ++, whereas Hakone is 1hrs ++. In terms of distance, they don't really differ that much.
Should i decide to return on summer before November, perhaps i can do this itinerary:
Day 1 : Osaka - Toyama ( 4hrs )
Day 2 : Toyama - Tateyama Kurobe Alpine route
Day 3 : Toyama - Kurobe Gorge - Nagano
Day 4 : Nagano - Hakuba (Happo Ike)
Day 5 : Nagan0 - Matsumoto
Day 6 : Nagano - Tokyo
Day 7 - 12 : Tokyo
Wouldn't this be a sound itinerary focused on hiking?
But do convince me if tateyama and Kurobe is worth the time for the detour in May. What's so good about it, compared to Hakone?
My main gripes about the detour is the extra transport cost that can shot up to 10,000 yen ++, and that toyama has nothing going on for it really. It's a small town around the alps. If i do it, i have to carry extra 3kg winter wear with gloves and hat on my 80L backpack.
If i do Hakone, it'd be cheaper overall with 2 day pass from 5140 yen, and Hakone ropeway is known as 2nd best in Japan. I can also do a short trip to Yamanakako from Gotemba, or even revisit Kawaguchiko on my 3rd last day in Hakone. Besides, i can see the sulphur valley in Owakudani, as opposed to Jigokudani which is still covered in snow. If i'm bored, i can do light hiking there on Komagatake. There's also a nearby Jinja in Hakone.
If i have to be convinced that Tateyama is worth the trouble, it'd be that the view has to be breathtaking enough for me to wake up earlier twice during my time in toyama.