I have lived here since the early 90's and had no idea this hike was right here or I would have definitely done it sooner. I had seen the path heading behind the building but thought it was for something else... I really wish more of the trails around here were marked better.
Upper Falls is located just east of Bridal Veil Falls in Provo Canyon. The internet tells you to park in the Upper Falls Picnic Area parking lot (accessible from the Bridal Veil/Nunn's exit) and cross this foot bridge (pictured above) over the river. Unfortunately, it is blocked and says No Trespassing so I would recommend parking at either Bridal Veil or Vivian Park to access the trail head via the Provo River Trail. The trail head is located behind the old pump building (pictured above) and it is very rocky. There is one fork in the trail so stay to the right. It goes straight up and is pretty steep, but don't worry, it's short.