First all, there's a good day hiking map of Yosemite Valley by the Park Service at
http://www.nps.gov/yose/planyourvisit/brochures.htm
(click on "Yosemite Valley Hiking Map")
Here's some suggestions:
* From Yosemite Lodge, hike up the Yosemite Falls Trail part way to Columbia Point--great view of Yosemite Valley. Start at the trailhead west of the large restroom building near the road at Lower Yosemite Falls. Takes about 3-4 hours (2 miles round trip, 1000' feet up)
* From the same trailhead, hike to Lower Yosemite Falls. Only takes a half hour.
* From Yosemite Lodge, walk on the bike trail along the Merced River to Swinging Bridge. Then head east to Yosemite Chapel at the old village, then cross the footbridge back to Yosemite Lodge. Takes an hour or two.
* Take the shuttle bus to Happy Isles (or walk to Happy Isles from Curry Village). From Happy Isles, take the Vernal Falls trail to the bridge over the Merced River--there's a good viewpoint of Vernal Falls upstream. Takes about 3 hours, including time to get to Happy Isles and back.
Print out the Valley hiking map (above), and the second page, which describes most of these hikes and others, to choose from.