The first and most obvious difference between a vacation at a beach and a vacation in the mountains is the climate. In the mountains, there is an excess of fresh, dry air, and at a beach, the air is humid, and might be polluted slightly. It is important to keep in mind that the higher you go in the mountains, the harder it might be to breathe, because of the elevation levels. If you are sensitive to this kind of air intake, it might be a better idea to vacation either on a low mountain, or on a beach. The beach has a blazing hot sun beating down on you during all daylight hours, whereas in the mountains, it is not necessarily freezing, but incredibly close. You might encounter some snow in mountainous terrain, especially the higher you travel on a mountain, but never at a beach location. In mountainous areas, it is often cloudy and overcast, especially in the land surrounding them. It might even rain during most of your stay there, considering your vacation be only a week or two long. However in a beach area, a sunburn is usually what you take back home as a souvenir. It is highly unlikely that you will get rained out on a beach, taking into account the location of the beach you choose to stay at. If you are looking for a warm place to sunbathe, the beach is the place for you. If a cold climate is more your thing, then look towards vacationing in a mountainous place.
Activities that you can do in these places are varied. If you are to vacation in the mountains where it does snow frequently, skiing, mountain biking, and snowboarding are well known pastimes. In addition to those activities, you can also ice climb and snow tube