Be respectful and minimize your impact. St. Paul parks require that you obtain an annual ice climbing permit. The permit requires a signed waiver and a fee. There has been dialogue with the city about this requirement and many climbers do not agree with the fee. For more information on this access issue see discussions on MN forums.
A nice ice climbing area if you are too lazy to drive to Lilydale. The ice is not always climb-able since the falls get good sun and run off from the road. It is only a three minute walk from the road to check conditions I find it worth a stop.
Brideveil Falls is on the NE side of the Franklin Ave. bridge. There is ample parking and there are steps going to the bottom of the bluffs on the SE side of the bridge, or you can hike through the woods.