My mountains are the Appalachians. They're some of the oldest mountains in the world. Compared to the Rockies they're probably just foothills, with the highest peak being only about 6600 feet above sea level. I've been to the top of that mountain, Mount Mitchell, although it's mostly a drive followed by about a 500 foot walk to the actual peak. It's usually cold and damp up there, which makes it a great place to be in the summer. Although not nearly as tall, Mount Pisgah makes for a more challenging three mile round trp hike, a hike I did every year for thirteen years.
The mountains around here are most beautiful in May, when everything is at its greenest, and October, when all the leaves change. I usually hit the Blue Ridge Parkway in May and give it a miss in October, because that's when all the people from far away exotic places like Florida and South Carolina show up and demonstrate their fear of hills, curves, and Parkway etiquette by driving very slowly and refusing to pull off at overlooks to let anyone around them. The mountains are sometimes quite pretty in the winter too, but I usually miss that because when the weather makes them pretty it also makes them dangerous to travel on.