Beautiful nature town outside of Tokyo?

Hello. Does anyone have suggestions for a small to medium-sized town that is within 2.5 hours by train of Tokyo? --There are countless options, I know, but I'm mostly seeking a place that is in a beautiful natural setting, preferably mountains. Maybe an onsen town. A place that has a few good options for food, and some natural sights and opportunities for walks or hikes.
The context: Me and a group of friends (5-6 people) will be meeting up in Japan in May, from different places around the world. One of those friends lives in Tokyo (though knows very little about places outside of the city). I am looking for a place we can all meet to get out of the big city for a few nights, and be somewhere beautiful where we can relax and have some nice dinners together. We would like to avoid any large crowds or very touristy places, and don't want to have to take a lot of buses (and no ropeways) to get around. Budget is flexible.
I've been researching on this website, and have some ideas:
Karuizawa
Bessho Onsen
Kusatsu Onsen
Minakami
Nikko (too touristy or large?)
Shima Onsen (maybe too hard to get to)
What do you think of these places meeting my criteria? Or, do you have other places that you recommend? Thank you for your time!

It has been pointed out that I over-recommend Karuizawa so I wont, even though I think it is probably a great choice.

The towns that you have listed are quite different, I havent been to all of them, my input is this:

Nikko - nice, actually I think it is nicer in winter with snow. Not that much to do there I thought
Karuizawa - OK, I lied, I will recommend. Great choice of restaurants, some nice hikes, handy to Tokyo, but not as much history there (except there is a nice trail to walk that follows the Nakasendo Way).
Pretty reasonably priced hotels, good trinket or brand name shopping, if that floats your boat
Bessho Onsen - very nice and a chance for late sakura there, also cheap ryokan stays. Not sure about hiking though. Probably only go if you want baths
Kusatsu Onsen - can be warm there later in May and be careful to make sure your room has air conditioning (caught out on that one). Fun at night but you'd get more out of it if you are keen for the onsen.

I would also consider Kamakura and Enoshima (huge fan of Enoshima) or Takayama which is probably a bit outside of the 2.5 hour limit. But then even Nara is 2.5 - 3 hours from Tokyo and that would be perfect.

Is renting a car on the spot an option?

If so, I would recommend Nasu, but to stick to a road called Itamuro Kaido, because there is way less crowd and traffic there even during Golden Week. The road is fairly flat and reasonably wide, compared to a lot of other roads in the mountains.

Since it has less traffic, it is easier to drive through even if you're from out of town. There are rent-a-car offices in front of the Nasu-Shiobara Shinkansen station as well as Kuroiso local train station. You can also look into JR's "Rail & Rent-a-car" discount service.

Itamuro Kaido has everything from small stylish stores to cafes to bars to day-use public onsen to a nice resort hotel with an art gallery, and of course entrances to hiking or walking courses. You can ask for a less crowded road that would lead you all the way up to the oldest onsen in town.

And wherever you go in Japan, please don't drink and drive as you can always ask the bar to call a "daiko" service in which a car and driver will come to pick you and your car up for a fee as reasonable as a taxi one-way fee.

Meanwhile, if your friend in Tokyo lives on the southern or western side of the city, Hakone could be another accessible option.

By the way, I also love the Shonan sea resorts such as Kamakura and Enoshima, but those are not "mountains".

Izu peninsula would be an other option.
Or Yamanakako

Lots of places on Izu Penisula. I had a weekend holiday to Shimoda and hardly anyone around. Hydrangea season at the gardens was great. Some good history too. Stayed at one of the beach resorts (out of season) so very quiet and cheap.
I am thinking of doing a short holiday to Tsukuba soon (when work allows) - not especially small, but it's something I'm interested in checking.
There are small towns with onsen dotted across Nagano. Kamiyama/Togura I go to quite often - rural setting, not particularly expensive.
But within 2 1/2 hours, that covers a huge area. You could even pick one of the smaller towns "in" Tokyo and be far from the bustling city, but still a short train ride away (Ome, Oku-Tama - pretty small).
Enoshima - I tend to do that as a daytrip rather than a stay.