There are no bad views of the bridge from the south side of it (once you've walked across it); one option is to walk across the bridge, so you're headed south, then bearing right you'll walk on on Calle Tenorio (the street closest to the Gorge), soon you'll find a casa (I forget the name, but see Jean's post below) on the right (gorge side of the street) charging a modest admission price that's worth it as the back of the casa opens up to a spectacular view of the bridge back toward the northeast.
Another view is, after walking south across the bridge, linger at the view plaza on the left. Then continue to Casa Don Bosco mentioned in the above paragraph, which will be on the opposite side of the gorge, with you following Calle Tenorio.
BTW, in spring 2019 the trail down is blocked because of landslides caused by winter rains, it blocked the trail but hopefully will be open by the time you're there.