Just up the road from Bridal Veils Falls, is Upper Falls Park. The mixed oak woodland along the road borders the riparian habitat along the river. The mountains to the south are covered in aspen and conifers, in between cliffs. The falls are just to the west of here while a small dam on the river, controls the flow here.
There isn't a ton of data for this location which is only open to the public form April through October. This is really the best time in the mountains anyways. Along the river keep an eye and an ear out for AMERICAN DIPPER which love the fast flowing water here. WARBLING VIREO, YELLOW WARBLER, and SWAINSON'S THRUSH are usually hear, and often seen in the trees. BLACK-HEADED GROSBEAK, BULLOCK'S ORIOLE, and AMERICAN GOLDFINCH add some color to the trees. Looking skyward you will probably see WHITE-THROATED SWIFT and VIOLET-GREEN SWALLOW. Since BLACK SWIFT have been known to use the area, it is a possibility from here as well. FOX SPARROW, GRAY CATBIRD, and WESTERN TANAGER might also be found while you're looking around. During the winter if you are passing by, BALD EAGLE are often found in this area.
From I-15 exit 272 in Orem for 800 North head east on 800 North for 3.6 miles. Take the ramp on your left onto US-189/Provo Canyon Road and go another 4.8 miles till you reach the right turn down to the park.