The Swinging Bridge, so called because it goes to both sides of the river, is an excellent spot from which to see and photograph Yosemite Falls. You'll pass this view on the highly scenic Sentinel & Cook's Meadows Loop, and there's also a parking lot near the bridge, in case for some reason Yosemite Valley isn't a pretty enough place for you to take a stroll in.
If you cross the bridge and continue along the trail (also a bike path), it will lead you in a mile or so to Yosemite Lodge and, just across the road from the lodge, to the trailhead for Lower Yosemite Falls itself.
If you're feeling an urge to dive through your monitor into this picture - alas, this website is unable to help. But you can download larger versions of the photo to use as your desktop wallpaper.