Here in Colorado, we call the things in front of the Front Range the "foot hills." Some of them are 10,000' tall and they have some of the best climbs because you can go from plains to summit, whereas in the "mountains," the valley floors are often higher. In Summit County, we have 9,000' base elevations...

Generally, I think (and I mean MY definition) a mountain needs to be part of a range, caused by a geologic fault, or a single cone formed by a volcano. Our foothills are really mountains.