First, a week is well spent in Yellowstone and Grand Tetons with dozens of day hikes etc. Elk are in rut so they'll be more visible, more aggressive than usual. Plenty to see and do even if you don't like long hikes...
If you must, maybe hop over the mountains out of the Northeast gate on Bear Tooth Highway to Red Lodge and circle back through Bozeman or the other way through Chief Joseph Highway. If you're more interested in mountain scenery it might quench that thirst though Grand Teton's are very picturesque and there are numerous easy hikes.
-Mark