I have been on and up many mountains. You can take long walks up mountains. You can grab the rocks with your hands to go up. Some people even ski up them! (Not me though.) They are delightful even just to look at! It's so easy to have fun with mountains.
Ah, a mountain. Look at it. Doesn't it carry the majesty of all the world on its shoulders. (Get it, because a shoulder is a land feature on a mountain...) If the weather is right you can watch so many clouds dance around a mountain peak, and in the spring and fall you can see the snow-cover change in such a jiffy! Honest, summer is possibly the time when looking at mountains is the least fun. But summer is very important with mountains for other reasons.
That's right, we're hiking! Trails abound, the mountains are the place to be. Some proper trails go all the way to the top of a mountain. Other times, only part of the way up. This is especially the case if the rest of the way up the mountain is a scramble (more on scrambling in the next section). But often, a maintained trail will lead to some nice viewpoint, lake, or waterfall. Some trails go over a pass and then keep going. In this case, you usually need another car to get back around to where you started.
It's kind of pretty dangerous, but everyone treats it like it's not. Probably not a great idea.
I have done my share of rock climbing in the mountains too. It can be quite incredible, and also incredible how long it takes to go up 50 feet when there's nothing but a sheer rockface to "go up." I'm a bit out of practice now, having not been the climbing gym for many years on account of a) the pandemic, b) my general health otherwise and c) not as fun as it used to be.
I only do this in one direction (down), which is to say, the other direction (up) is done with a chairlift. Some folks ski both ways. I neither have the equipment to do so, nor the desire to go uphill into places where avalanches happen.
Cross country skiing is also fun.