Nice thread, Roberta. My favorite spot in all the world? Mount Rainier. Here's a link to a webcam, to see how the mountain is doing right now:
http://www.nps.gov/mora/index.htm
There are loads of websites about "The Mountain" and plenty of photos that show some of its appeal, but to me it is "my" resident mountain -- I can often see it while I'm out and about. Sometimes I think I like it best when there is a mist hiding all the views but the flowers & trees within a twenty-five foot radius; sometimes my favorite spot may be at Sunrise Point late at night while enjoying one of the most magnificent skyviews available. Usually, I like it best when I'm above the treeline on a warm summer day and a slight breeze blows over the glaciers to keep us cool as we hike. This first photo is from Rainier's most famous place, Paradise Park. It is a good dayhike is to that dark green triangle in the distance, just below the summit.
After climbing part of that distance you can turn around, look south and see the crater which is now Mt. St. Helens and "little" Mt. Adams, a mini-Rainier in shape, about 2,000 feet shorter and the second tallest of the Cascade peaks.
From Sunrise Point, elev. 7000 feet, it is said that you can see five Cascade volcanic peaks, each over 10,000 feet high. Mount Adams, shown here, is closely associated with the Yakama Tribe; Mount Hood (I've never seen it from here) is a hundred miles south and in Oregon. Closest summit is Mt. Rainier, about ten miles away. North are two more big peaks, Glacier Peak in the North Cascades National Park and beyond that, Mount Baker, which is very near the Canadian border. Here's Adams...
And here's a view of "The Mountain" that I might see while driving around near home.