One of the great locations to see the Upper Yosemite Falls is from Swinging Bridge. The bridge crosses the Merced River right next to Sentinel Beach on the Southside Drive (as you head towards the Village).
I am not quite sure why it is called “swinging” as it appears to be quite firmly constructed. The boards do shake a little when someone walks across, not good is you are using a tripod.
As you can see, rather than standing ON the bridge (which offers great views), I scrambled down river a little to get this perspective. You can see Yosemite Falls in the background.