The ouse runs through town, the main bridges, Ouse, Lendal and Skeldergate all have decent angles on them from the path next to the river.
EG Lendal Bridge:
Walk a bit further out of town (only half a mile or so) and you've got Millennium bridge which is a bit different:
Waterfalls you'll struggle with in town, but slightly further afield check out Falling Foss and Mallyon Spout, both on the moors not far from Goathland.
Back in York have a wander around the Minster, they're really relaxed about photography, no problem taking a tripod for example, and some stunning architecture.
The Nave, York Minster by
mark_mullen, on Flickr